I used to use PetLeash, but that addon was abandoned. someone made one called BattlePetLeash, but that one has disappeared completely.
it had profiles so you could auto summon specific pets on specific chars, or set pet swapping rules for different chars. it was really handy but i haven’t found any kind of replacement.
I’ve been using BartrubySummonPet since PetLeash broke. It’s less configurable, but I just need it to keep the same pet summoned at all times so it works great for that.
It does let you set a different pet for each character at least, and there are a few options for summoning based on mount, spec, or equipment that I’ve never experimented with myself.
that was actually all i was really after, thank you for the info/help!
Hey Minding! I’m not sure if this is what you’re looking for, but I’ve been loving this Weakaura I found:
“Permanent Companion Pet” will summon one of your favorites to follow you along if you don’t have a companion pet out 
I’ve tested it for quite awhile and haven’t had any frame/lag issues with it.