The road to Yosemite from Mariposa along the Merced river is limited to a short length. You can not tow a trailer or drive a motorhome in via that route. The east entrance near Lee Vining may or may not be open at the end of June. It probably will be this year because so far there isn't much snow.
Two years ago we stayed at
yosemitepinesrv.com near Groveland. Clean, very quite during late off season. Some pull throughs, but we backed in. Pool, showers, laundry. Small petting zoo was nice if you have kids. It is a bit of a drive into the valley, but we didn't mind. This was our first trip with hookups, which was the main purpose for the trip.
If you go up the hill from Don Pedro Lake towards Groveland DO NOT make the mistake of going up Old Priest Grade. It is way to steep to have a trailer on that. Stay on the main road.