It sounds as though you were talking yourself out of a TT. Your time limitations and desire to pull a boat would discourage me from taking on a TT, if I were you. How would you pull both the TT and the boat?
Maybe a utility trailer with a closed box on it would be a good alternative for you. You could pile all your tenting gear into it. We have friends who built theirs like a chuckwagon, with a pull-out kitchen and lots of storage. Or a teardrop, used to haul stuff, with a little kitchen at the rear. Cheaper than a TT.
But maybe renting a cabin would be easier than packing, schlepping, and wrestling with camping gear, and in the long run, less expensive than a TT. And if you're concerned about who has slept in the bunks, bring your sleeping bags - that's what we do.
Although the idea of a pop-up is a great one. Plenty of room, lightweight, not a lot of work, and you can carry a shower/outhouse tent for the Luggable Loo.
I agree that whatever you do, your kids will benefit by being outdoors.
