Thanks for the recommendations. I've stayed away from Card Wars because it seemed a bit expensive for what you get, and I didn't want to get sucked into buying multiple sets and booster packs. Maybe I'll have to give it a second look.
I want to play Fluxx, but don't really want to buy it because it's such a polarizing game. If I buy it and hate it I'll be <sad_face_emoji>.
I didn't realise Fluxx was so polarising. I don't think I've come across someone who outright doesn't like it. One of our friends wasn't a huge fan of bears vs babies though. Keep in mind Card Wars is only a two player game though so if the kids ever play without you or sometimes only one kid wants to play it with you it might be a good choice, but it won't work with three. Also (while I can't guarantee your kids won't pester you for them) you don't need to buy multiple sets and booster packs for Card Wars. One base game works fine. I'd just give it a look and see what you think. It isn't one of my absolute favourites by now (so there might be better options out there for you) but it is solid and it is fun to play with my nephew who quite enjoys it.
There's also junior versions of some of the games too. I haven't tried them out but if you like Carcassone or Catan but don't think your kids are up to the normal version yet, I know those have junior versions.
We actually have Carcassonne Jr, but they're starting to outgrow it a bit. It was good as an intro game, though.