There is no such thing as "The RetroPie".

Raspberry Pi is the hardware; RetroPie is the software operating system that is installed onto it.

The easiest and best way to play Amiga games on RetroPie OS is to make sure the P-UAE core is installed. I don't recommend installing experimental packages or standalone emulators over just installing the Libretro cores themselves, because the cores allow you to use the Libretro shaders and by using Libretro cores, it means you can manage your preferred settings globally across all cores.

No worries, hope you and your kids enjoy whatever you find.

Snow Bros, Zupapa, Bang Bang Busters, Tumblepop and Don Doko Don are great kids games on MAME. Others already mentioned Frogger and Rod Land.

Also fantastic, but a fair bit more difficult, are Kickle Cubicle, Pang (aka Buster Bros) and Solomon's Key.

Also check out Funky Jet, although it might be deemed to 'aggressive' by some (beating enemies with boxing gloves while jetpaccing around).

For kids a bit older, Top Hunter: Roddy & Cathy might be fun, as well as Spinmaster.

That worked! Took forever to update the script but once it finally finished and I did a reboot there it was. The new emulationstation black loading screen and the random button. Very exciting thank you very much!