In late May you probably won't face the huge crowds one sees later in the summer. But you may find your explorations somewhat limited because of lingering snow. My mother worked at Old Faithful for more than a decade and I remember pictures she had taken in mid-May and they had dug through the six feet of snow to get to the front doors of the store. Not like that every year, but snow will undoubtably still be around.
Parking near Old Faithful won't be a problem with your rig as there's a huge parking lot there. There are big rig places to park in Mammoth and you can hike from there. Same with Canyon although not at Inspiration Point. I remember there being RV/bus parking at Artist Point on the south rim of the canyon.
You'll be challenged when it somes to some of the other geyser basins. Parking near the Grand Prismatic Spring is particularly difficult, even in a car, as there simply aren't enough spots.
I don't know if you have or use them, but bikes are an amazing way to get around and avoid some of the parking crowds. When we were there in mid-July parking at places like the Lower Geyser Basin was backed up a long ways. We simply drove a mile or so up the road, found a paved pull-off, got on our bikes and rode back to the parking lot. (Traffic is pretty slow so really not very threatening) Locked our bikes, hiked the trails, and got back to our bikes. We saw cars still waiting to park that were in line when we got there.
Bikes are also really handy around Old Faithful. One can ride along the old road from Old Faithful out to Morning Glory Pool. We would check on the predicted eruption schedule in the Visitors Center, then ride out the road, park and lock, then hike to the geyser. Had several people offer to rent our bikes when they saw how much walking we saved.
One more thing: if at all possible try to get that 18 year old to go along. As you know Yellowstone is one of the marvels of the world. She won't be disappointed (although I can't promise how the drive out and back might be! ;) )