Sorry to hear about your father, and your work-from-home. One of the biggest issues with getting work-from-home approved in the first place was a distrust that people would be actually working.
I was lucky - I'm IT and we supported all of the Americas, so we were kitted out that even if there was a blizzard, we could work remotely. Because we already had things in place (read: they wouldn't have to spend any money), we were tapped to pilot work-from-home in 2015. And because measurable productivity went up, we were allowed to keep doing it. Here's a bit of what made it work for us, but it assume white collar office work.
But it was a large adaption to get used to it, and we lucked out with our big bosses who set the expectations not only among us, but up the chain. First, we were very results oriented as opposed to hour-oriented. And those tasks were measurable. So they could see milestones getting done and didn't care if someone took 10 minutes to say Hi to their kids when they got home from school or finished something after dinner. This really critical, because otherwise there isn't a sense of things getting done to senior management. Hopefully you already project managers or KPIs with baselines of what they can reasonably expect while you are in the office.
Second, get a work instant messager. Plenty like Slack out there everyone can hit over the internet. Being able to chat with people informally is really a big thing. The equivalent of popping your head over a cube and asking a question, or chatting while getting coffee. And really call people you work with. There were times when we'd log three hour calls - 20 minutes of planning something out we were working on together, and then the rest of occasional chatting and connecting to the person, random "put our heads together" when having problems, and sometimes just companionable silence but there was someone there.
I put all ofthat in the past tense - my company has been acquired and the new company doesn't do work from home ... but I'm attached to the corporate head office in Denmark and have to work remotely with people anyhow so I've managed to keep it going. Which is good, commuting to the new office would steal about two hours from my life. And I appreciate it - there's always been the "need a few more minutes" and work late (salaried, no extra money), but going above even that now and then is more than worth it to avoid the commute time.
So I guess the advice can be summed up as: get them focused on deliverables, and make sure those flow, and get instant & informal communication set up among your peers and the people you work with.