Well my go to for getting my kids into fish are minnows.. though they are NOT easy to store.. and if you think worms are too much of a pain.. Minnows are much worse!! Worms are actually really really easy to take care of :/
Anyway with those not being options.. I would suggest the Berkley GULP products. They are very similar to live bait.... But not actually alive.. just rubber soaked in scented oils. The container looks similar to that of powerbait.(They are known to leak out the scented juices so keep it in a ziplock bag or get a jar or something to keep them in or the juices will leak all over your tackle bag/box... and they smell pretty strong LOL)
I just put a small GULP minnow/Fish Fry/ets(My favorite look like mini Curly tail grubs, not sure what there called) on a very small jighead(Like an ice fishing ratso jighead) and put that under a bobber. (Distance from bobber to jig varies)
If your 2yr old is like mine.. He cant quite cast yet?? Even so.. Just cast it out for him and let him reel it in slowly... My 2yr old caught a gill on the 1st cast last time i took him out!! I casted for him and turned around to bait my 4yr old sons pole and when i looked back my 2yr old was already battling a bluegill!!
Hope that helps