All good stuff

If you wouldn't mind

Could you tell me of the quest your group is currently doing and how it's being handled?

Also, how do you handle things where you want your group to split up?
Heh. I'm laughing at myself because what I'm doing is a bit complicated and involves both a lot of multi-part arcs and a lot of improving. BTW, I'm not sure what system you are looking to run in. A D&D (or D&D-like) game will have different focuses (such as greater combat focus) then a bunch of other games out there. I'm currently running 13th Age, which is a D&D-like. I'll try to put some references in D&D 5e because it seems to be a lingua franca here on EN World.
I have the habit of throwing multiple options at the group, seeing which ones they want to follow now, and others, well advance without the PCs interfering (though others might). They pick up threads, put them down and do something else, and then pick them up later as something new comes in. As time passes I keep my world dynamic by having lots of plots and consequences (good and bad) of earlier adventures still moving. This is more campaign management then adventure management, but it does influence my adventures.
OH, if any of my 13th Age players are reading this, stop reading now.
So, right now the characters are mid levels (about 11th in 5e terms). The players already know that the dwarves have been chased out of the Underworld ages ago when the drow released a mind/spirit-twisting poison that is still making the underworld uninhabitable by anything sane. (And there are character plot hooks that are connected to that.)
At various points during their earlier adventures, they had helped diverse groups of druids get branches from these enormous petrified trees called the World Pillars that hold up the sky.
Recently, the High Druid, a very powerful pseudo-patron of the group, has told them that she was collecting those branches for a grand ritual because she wants to grow a new tree, an Axis Mundi (think Yggdrasil) that will connect the Underworld, the land, and the Overworld and will help drain this poison over time (many lifetimes). She'll have to kill herself to fertilize the tree, and no it's not like she'll go into it. She blames the Lord of the Dwarfs that they never got their "World Engine" working again to clear the poison.
I mention that because that's connections into most of the characters back-stories, between the High Druid and what's happening with the Dwarves, plus it's tying back to adventures they have already done. This fits the "players are interested in the outcomes" part.
Right now there's time pressure (why is irrelevant, just that it's there and not exact), but they need to retrieve branches from the last World Pillar, where the druids sent were all killed. So they know the stakes, know the time pressure. They have at their disposal a one-of-a-kind dwarven zepplin (actually it's hanging below a comatose sky whale from the Overworld).
NOTE: Even with the time pressure, the party took a several day side-trip to go to a city on the way and plan/commit a heist of books in a heretical book repository (so stealing from a good-aligned temple) that they needed for two other ongoing plots. This is part of letting them make meaningful choices. That time spent is acceptable if everything goes well, but there are unexpected twists ahead.
So, they get close to the Red Wastes where the last World Pillar tree was. Yes, was (but they knew that). Ancient history is that a bunch of demons from the abyss escaped and the first Red Dragon burned them all down, creating a land that is somewhat barren to this day.
Anyway, the petrified World Pillar took a while to burn, and raised a volcano with all the heat it dumped deep into the earth. The setting also has solid clouds that float around the Overworld that the giants like, and ghosts of sky roads that come out when the moon/stars is right. Well, they have a choice of dropping out of the skywhale a distance away, going through a petrified forest of it's saplings, and then going into the volcano to the stump, or going up to the solid cloud that's been there for ages that likely (but not definitely) was pierced by the tree and the ghost trunk still keeps here to this day. All they know about that is that snow falls from it. This is a imperfect meaningful choice for them - they have some ideas what each can mean, but not perfect knowledge to pick.
Oh, and I laid some pipe (threw out information that will be foreshadowing) about the magical currents all twisted in the air like some great magical creature was flying around.
They went up top, found a frozen giant-sized castle that seemed abandoned, and went in. After traversing through lot of magical cold-themed traps and avoiding the dead (well, UNdead, but they don't know that yet) frost giants who looked like they were trying to escape from the ice wall, they eventually got to the throne room. Part of the reason for the traps was to spotlight the rogue who took some anti-trap talents, part was to control pacing and ratchet up the tension, and part is to make it ...interesting... if they end up having to run.
I don't want to go into too many details of the fight, but a bit of lore that came up a few times is that wooden stakes paralyze vampires because a High Druid ages ago did a ritual to make it so. This was told to show how potent a ritual with the World Pillars could be ... so the players think. Really it was more laying pipe. There's a staked vampire (MUCH nastier in 13th Age then 5e, consider it around CR 18) in the tree, and the ice sorceress frost giant and her husband are something close to under having been corrupted living off the blood ice that drips from it.
Side note: All the time I throw out "important" things, like "all of the summoned demons were wearing a thin chain covered in runes". While often these are ports of plots, they are just as likely that I don't know what the detail is for, but building a later adventure I'll realize I can use it for a tie it. Is that chain a recurring summoner or a cult? Are the runes done in an ancient elven style? Whatever I need. Laying pipe is how I heard that described years ago - putting things in at the foundation level before everything gets covered over.
Back to the adventure. Going up to the solid cloud was the more direct route, which they knew (not having to traipse around in a haunted forest and then go into a volcano), but it's also the deadlier. By the numbers, this combat will likely kill some if they aren't smart, and many are already partially frozen (initialize penalty and chance for ongoing damage when they take more cold damage) from the magical ice traps.
They have a lot of ways to do this. Head on fight - risky, but if they play tight they could pull it off. Grab the branches and retreat out of the castle - made harder by the traps and frost giant ice zombies that will soon be coming out of the walls. Take the branches and jump out the viewing holes in the cloud - but less than half the party can fly. Oh, and unfreezing the ice-encrusted branches will take some time or magic, and doing it recklessly could release the vampire. (Which would actually go after the giants first, but would be starved and go after the party next.)
Oh, and I mentioned a twist about time before. The captain of the dwarven zeppelin was told about what is being down and sees it as usurping the Lord of the Dwarves' right of command he asserts over the Underworld (regardless that he can't enforce it) and has unloaded a crate of food/supplies and has flown away while the party has been in the castle. So hopefully they don't come running out hoping to make a quick escape on it.
Just for comparison, the lower path was a several day trek through a haunted forest, but not nearly this deadly with the individual things that came up but time pressure would be mounting, to the volcano which would have it's own heat-related issues, only to find out that the inside was a Red "Hordesong" Dragon's lair. It was out, but the Hordesong dragons sing to their treasure and it sings/reverberates back and they can tell if a single copper is missing. The stump is not part of it's treasure, but several characters would have been SOOO tempted by horde they were passing and if they took any I could add a powerful dragon tracking them down as they fled back to the High Druid (now on foot).
So that's the "current quest". There's more trials on getting back to the High Druid - I'm basically seeing what they can think up on how to get down from the cloud, with a backup plan of the trunk materializing like the sky roads when the moon is right as a backup plan - but only after more time has passed. I'm confident that they can work out something quicker. And I haven't detailed about getting from where they are back tot he High Druid's woods - if that's going to be a multi-session adventure with time ticking or a montage and some skill checks that takes half an hour will depend more on what the players are interested in (and if they are being actively pursued). If it does end up taking multiple sessions, I'll probably have another arc intrude and they'll have to decided to follow up on promicing but short-lived leads or continue and hope they get back quick enough. All of that, including the idea of "let's nto spend a lot of time on this if it's not interesting" harkens back to the "path to get there".
Completing this will have long term changes on the game world, which is a reward for some of the players. There will also be more immediate rewards for them, but much more likely boons like being able to soothe or command animals, giant eagle mounts, being able to do Tree Stride or something like that, since the High Druid isn't very into magic items. Plus a bunch a big lead on another campaign arc that they don't realize is connected yet.
Oh, and the emissary will likely have a chance to earn a new name. The character is a barbarian where they earn their names, and ended up trading his name in a goblin market for a ancestral bow of his clan that he wanted to return. He has no knowledge of his previous name and it doesn't feel like it describes him to himself anymore when other tell it to him. Ah, fun.