Great idea! Hopefully this post can serve as a running list for other user's recommendations. For now, here are some I know of:
I've got a 3 year old and she loves Donut County on the iPad. I personally haven't tried on a Polycade, but I have a friend who played on his and said it was really fun watching his son use the trackball
You might also want to try out Pikuniku (2 player co-op) with your kids. The same friend had a really good experience playing that. We'll have that in the AGS Store, but you can get it on Steam too.
My last recommendation is Unravel Two. I haven't played but another friend who has 2 kids said that's their favorite game to play together and highly recommended it. Unfortunately, you'd need an XBox controller to play 2 players, and according to my friend it's way more fun playing coop with your kids.
And just in case you want another game that's good for kids, I really like ThinkRoll Space on the iPad.