It's certainly feasible, unless there's something in the bylaws that require you to be on site during business hours, but I've never heard of that.
I think the main issues are how many patients you're covering at each, and how far away they are. Rounding at two facilities isn't hard at all. Taking admits at two facilities on the same day is, as that could require a lot of back and forth. But you do have 24hrs to do your H&P, so you could always round at facility 1, see any admits that have arrived already at facility 1 (or at at the acute care hospital if it's a unit in a hospital), then head over to facility 2 and round, see facility 2 admits. Then you either circle back to facility 1 to catch any remaining admits, or you just see them in the AM when you round.
Dealing with nursing at two facilities, different EMRs, etc, may be a bit of a pain, but are all workable.
Having hospitalist coverage will help significantly as well.