luvmyfam,
After we had a popup and the kids wanted to take their bikes camping, we "invested" in this bike rack:
http://www.prorac.com/tenttrailerpro.php
Note that I used the word "invested" because it aint't cheap. But we are state park/Fort type campers so every time we go out is an opportunity to bring the bikes.
We have an arrangement like the top photo in the link where I take the front wheels off (quick release) and the back tire rests on the front storage box. We got the optional pads for the back tires so the tires don't leave any dark smudges on the storage lid.
Like you we are a fivesome family so we bought the 4-bike rack then got the additional skewer kits to carry up to six bikes. These are listed here:
http://www.prorac.com/tenttrailerapps.php
I didn't want a rack that put holes in the roof because that's where the leaks will be WHEN they start (not if). I didn't want to have to lift the bikes over my head to get them on top of the tow vehicle. I didn't like the hitch solutions either and bikes behind the axle on the pup could create sway (bad news). This rack bolts on pretty simply and will of course add some tongue weight to the hitch. At the time we bought the bike rack we were towing with a Chrysler Town & Country minivan.
I try to offset that tongue weight a little by packing some items inside the pup before we leave BEHIND THE AXLE to provide some counter-weight. Things like folding bag chairs are what I can get back there.
Having the bikes has been great for us and gives the kids some freedom. The rack is now around $400 for the 4-bike and the accessories will be a little more. So like I said it ain't cheap but it works dang good. I have no experience with the accessory that lets you keep the front tire on but if your kid's bike are NOT quick release front tires, this may save you the tire off-tire on work. The front wheels either go in the pup main side door closed up or in the back of the TV (Suburban).
Just another alternative to consider.
Bama ED