Where are you located?
I understand your concerns - coyotes, sunlight, depression...
It sounds like your goats safety is very important to you. If you need to leave town - and it happens, we have emergencies - then please keep the goats locked up with a lot of water and hay.
Had a tornado rip through here last Saturday night. Lots of damage, lost some housing and pasture fencing. As much as I hated to do it, I had to leave the turkeys and the guineas in their house for three days (Sun, Mon, Tues) before I get a suitable safe structure in place to move them to. Even though I attempted to clean their space, and the windows were open some (it's been below freezing here), the ammonia smell was enough to wake ya up. Better the not so pleasant smell than dead. ALL of my animals appear fine. Three days locked up didn't kill them. I did visit 3x a day because I could.
I think your goats will be fine. The fact that you care so much for their safety will help too. Make sure the space is clean and secure before you leave. Plenty of water and plenty of food. When you get back from your trip, go check on them. Let them out, even if it's for 30 minutes.