A 12-year old and a 6-year old huh? I wonder just how sophisticated 6-year olds are nowadays.
I suggest Contrast. It's on PC (Just over $11 for the next 24 hours on Steam) [http://store.steampowered.com/app/224460/] and will work with a 360 controller [http://steamcommunity.com/app/224460/discussions/0/648814843739781072/].
The game is slow paced, has excellent art direction, and doesn't not punish you much when it comes to timing and collision detection. Actually, it's easy to die in the game, but you restart almost immediately and from close to where you left off. The puzzles may stump the younger sister, and you may have to step in and give them a hint sometimes. Overall, it's a fairly short game that won't hold much appeal for adults, but I think kids will take to it more. Also, there's a few scenes with some thugs and one scene with a gun, and it's possible to see the mother character shoot the father, but he lives (also, I think it's an easter egg). Everyone but you and the little girl are depicted as shadows.
My default go-to for stupid fun are the collective works of Justin Smith [http://www.captain-games.com/], creator of Enviro Bear 2000. His games are simple, small executables which you can download for free. Enviro Bear is just bizarre, and other titles like RSSS (Realistic Summer Sports Simulator) are really good for a laugh simply because the games are so one dimensional and hard to control. All of his games are usually mouse-controls only, with a few keyboard inputs.
Unfortunately Botanicula has no controller support, but it's all mouse controls. It's also adorable, and a very, very cute game that's worth playing for both adult and children. I also recommend Samorost 2, and the first Samorost [http://amanita-design.net/samorost-1/] is free to play and works in a browser. Again, sorry, no 360 controller support.
Aside from those, I don't know what to recommend. Trine or Trine 2 perhaps? Wouldn't that be surprising if they showed up and asked if you had GTA V.
