Dog and cat should have a homepoint system, which will make it so they wont wander away too far, and create a guard dog/cat.

Petting your pet, original idea from Quark, shift-right click with an empty hand to pet them

Guard dog chase and kill skeletons, cats will actively go to a creeper to scare them, which is an improvement of vanilla cats where they dont notice creepers at all, however, cats wont attack creepers

The mod that have an actual complex mechanic for caring of pets is Mo Creatures and their kittens, so maybe Amimania could copy some of the ideas? Play toy for cat could be a ball of yawn and for dog is a fetching stick.