We have 2 children and we "live" in our fifth wheel for 4 months out of the year. We camphost at a campground that is about 30 minutes from our house for the month of May and then we camphost in Maryland for the month of June and part of July and then go to the beach for a couple of weeks before returning to the campground for the month of August. Both DH and I are retired with a great income from retirement, but our kids are also in school and we transport them back and forth unless they have activities that require them to be at home for the night.
With that being said, the first month or two is great in the 5'er, but then after we are in it for about 3 months, it begins to get pretty small even though it's 38' long. (It actually has more square footage than we had in our first apartment when we got married.)
If you were going to be able to move around and see some of the country, I would tell you to go for it, but the fact that you are going to only go for short trips to 4 different campgrounds in the area that you live in makes it a much different scenario.
The limited amount of square footage in an RV SMALL compared to any house and I assume your child likes to have friends over on occasion to play. The kitchen does not offer lots of prep space, so cooking of large meals is harder to accomplish, but not impossible.
I enjoy not having to share bathrooms with my kids when we are home and that is not the case if we are in the RV. That bathroom gets really small when we are all 4 trying to get ready to go somewhere in the mornings and having to wait for 3 other people to get ready.
I have no complaints about our bed because I put a memory foam mattress in it when we first purchased it in 2009. It's still in great shape and it is the same mattress that we have at home. My girls now have to share a bedroom in the RV, but we have been looking at a 3 bedroom one. If and when we decide to take off and home-school the girls for a year, and go see the west, we will purchase something else.