While I agree with most of the other replies that it's going to be a little crowded in a class C it still looks like a good fit to me. As you noticed rental units have a good reputation. A small class will take you almost everywhere. It's better than a trailer for quick stops along the road and easy ins and outs at fuel stops. It will fit into the smallest campground and will be good for overnight stops at big box stores, truck stops and rest areas with sightseeing during the day. It's not a good idea to leave a unhooked trailer parked on one of these overnighting stops while you're sightseeing but dragging a trailer around all day will not be fun.
I'm looking at this from the view point of living full time in a small C but we've never had a trailer so my assumptions could be wrong. However we did fulltime for a year in a VW vanagon with a four year old. A four year old is a lot smaller than an eleven year old but a van is also a lot smaller than a motorhome!
Go to a dealer with your wife and daughter and pretend to live the different types of RVs. You'll get an idea of what will and will not work for you. Good luck with your choice!