I've never had a problem with Tiny Hut. I just enforce it as-written (one-minute casting time, ends if you leave its area, 9 creature capacity, Dispel Magic breaks it, etc.) and it works fine IMO. It's pretty handy for protecting the party from the elements when traveling, much better than a tent. Random encounters aren't really an issue. I check for random encounters twice per Long Rest...once at the beginning and once at the end. So if a random encounter occurs on the first roll, the encounter will arrive before Tiny Hut begins (or while the caster is casting it), and if it's on the last roll, the random encounter shows up shortly after Tiny Hut ends.
Same thing for Rope Trick....just enforce it as-written and it's fine. (Check out the parts about "the whole rope hangs perpendicular to the ground," "at the upper end of the rope, an invisible entrance opens," and "anything inside the extradimensional space drops out when the spell ends.") Unless they are carrying a length of rope only a few feet long, they might need to climb as much as 60' (4 rounds) just to get inside...and possibly take 6d6 falling damage trying to get out.