It's a very little known fact (mainly because the Park Service doesn't want it known) that there are a bunch of privately owned cabins behind the Wawona hotel, many of which are for rent by the owners. Long ago I rented one and it was fine.

Some of them are rented through this website:

http://www.redwoodsinyosemite.com/

This might well be another possibility. There are also condos for rent around the turnoff to Badger Pass that through an accident of geography are only accessible from inside the park but are actually just outside the boundary. I believe the building is called Yosemite West. These are more expensive.