A nice 5-8 year old popup with a 10' box should be enough room for you and your kids. Make sure there is no leaking or holes in the canvas/vinyl. Don't try to do the bigger popups with bathrooms, but get you a little potty to use for the kids AT NIGHT ONLY!
You should be okay with that being pulled by your vehicle.
I don't know where you are, so I used the Hudson Valley craigslist to look for a popup.
This one will probably weigh too much since a slide adds a lot of weight to the trailer.
Coleman BaysideThis one is 2600 lbs.
https://hudsonvalley.craigslist.org/rvs/d/2012-rockwood-popup/6582573795.html This one is 2500 lbs.
Whereas, this one in Syracuse would probably work since it only weighs 1700 lbs.
Jayco Quest