Embrace mobile gaming. Especially the classic Nintendo handhelds. I can rock my baby to sleep and play Pokémon Ruby on my GBA at the same time. Embrace RPGs and other games where reaction times don’t matter. If I’m sat in a chair with a sleeping child I can even play a game where reaction speed matters, like Tetris.
Get a flash cart so you don’t have to switch games or carry a library of carts with you. Keep it in your car for play if you’re out a lot. Oh, and get a decent modern screen mod so you can see the screen outside.