I hope you don't mind if I don't answer your actual question, but wouldn't it be a better option to sleep before taking your mom into bed, so you have sleep from 10 PM to 5 AM? What you're currently doing seems to equate to night-shifts, which are really bad for health, AFAIK. It would also help solving your problem of finding something social to do, I guess - that should be a lot easier in the evening.