If you are going to buy a trailer, then I would rent one rather than a motorhome. While they both result in camping, they have different positives and negatives and you should get a feel for what you will get.
A four night weekend would be great. You would have three full days to enjoy the camping. Even a three night weekend will give you two full days. That's enough to get a feel for how much you will enjoy it.
I agree about waiting on the nieces and nephews until you have a better handle on dealing with the trailer. I would wait until you buy, then do a couple solo trips with just you two so you can work out the little things. Then start bringing the kids along.
Most "6 people per campsite" rules at public parks will allow an exception for a single family unit. That means parents and kids. Not parents, aunts, uncles and kids. Depending on how many nieces and nephews you want to take and their ages, it may or may not be allowed. The two of you and five kids under twelve maybe one or two older - probably OK. The two of you and eight older teens - probably not. A ranger may likely question on the latter because it looks like it could potentially be a party situation or at least not a family unit. The former will likely be unnoticed unless the kids are causing trouble around the campground.
Partying is a big concern but also overcrowding of the campground. If there are 20 sites and every one has the max 6 people in it, that's at most 120 people that campground has to handle. Now put 10-15 people in each campsite and you are talking two to three hundred. The campground bathrooms and water (some areas have limited water because it's trucked in) can't handle that much. And many folks would try to cram 2 to 4 families into one site to save on the nightly fees, so that overcrowding is very possible without these limits.