Dog-trainer here has to say something about that - and about the topic of dogs and something we call “Prey Drive” 
In most service animal work (not necessarily guide-dog work, mind you) we seek out animals who have strong play and prey drive - this means they’ll chase, they’ll retrieve, they’ll play with humans. You won’t find better trained dogs than these working dogs… none of them would attack a child… but it’s very hard to stop them from “crittering” - running after rabbits, chasing squirrels - when they’re not on the job. On the job, they know they must not. Off the job, they’re dogs. Dogs with play and prey drive CHASE things. They pounce on their stuffed toys. They make their squeakers squeak. It’s hard for them to tell the difference… I once had an instructor - a police dogmaster who now trains landmine detection dogs - fabulous man - who told me that even the best of the best dogs will chase things… even with all their training. Your hope is that when you scream out a “drop on recall” down command, you just hope it’s stronger then their instinctive drive to chase prey - not kids, not other humans, not bikes or cars… furry creatures. In some dogs, it is - they’re that well trained and that driven to please. In others, they just can’t help it. Especially if they’re in their yard, unsupervised… Now, if they chase children, they have issues that should be worked on. Dogs who chase anything and everything can be helped and trained out of it - most dogs are, by their owners. But if left to their own devices, unsupervised… well…
In SAR dogs, it’s one of our common problems - dogs will like chasing squirrels because it’s fun! It’s part of their nature. We do curb the behavior, but it’s still part of the initial qualities we were looking for.
I wouldn’t make an association between a dog who attacks a bunny (though that’s such a sad story - I’m so happy the bunny is alive and mostly well! That must have been so scary…) and say he might have attacked a child.
There’s a difference between aggressivity and prey drive. A very BIG difference. In a fenced yard, a tamed family rabbit may not be able to escape. In the wild, bunnies sure as hell have given some of my fastest retrievers and sheepdogs a run for their money and have escaped unharmed. If a dog were to chase people - it would be a huge problem. It would probably have been caught EARLY in its life - as a puppy - and taught not to even DARE try. I have to do that with most of my high-prey-drive dogs. However, we do encourage them (as owners) to play tug, and to play fetch with stuffed toys… and to chase each other when they play… and to chase toys on a rope… so we reinforce the prey drive, but not the “humans are fare game too” drive, early. It’s a nifty distinction.
Anyway. As for the OP’s question:
I wouldn’t be surprised if the dogs returned, if they saw the bunny free in the yard again. Right now, your beloved pet (bless his heart!) is an easy target - no place to easily withdraw to, and certainly no previous “flight” experience from such situations. Dogs are quick and agile - a stunned bunny is not. The dogs found this fun - it’s a game - and though you scolded them, they may well return again. They’re getting something out of it - it’s self-rewarding. Ah, Skinner…
(Operant conditionning, anyone?)
With regards to invisible fencing for dogs: I’ve seen it work rather well with some animals. Especially calmer dogs who are very sensitive. I’ve also seen dogs with very strong prey drives run straight through the “fence”, get zapped, and continue chasing a squirrel across the street. Of course, you try getting the dog back HOME when that happens. They don’t care about getting zapped on the way out because, well, the squirrel is far more interesting… but coming back, they get zapped on the way in, too. I had tried that with my Mika, a strong willed Malinois with an incredible prey drive. She turned out to be one of the most incredible SAR and detection dogs I’ve ever seen. She was a hard worker, a hard dog… but a sweetie with people. Still, she had a no-nonesense attitude.
She once ran after a rabbit, straight through the invisible fence. Lost the bunny, came back, and sat on the outside of the fence, waiting for someone to turn it off before coming back in. Smart dog. The draw back into the fenced area wasn’t enough to warrant getting zapped again, according to her.
As for the rabbit - I’m so glad the bunny is okay! It’s such a hard thing, really - I can understand you would want him to get some outside time, it’s good for him! I’m all for a caged/maybe even a chicken-wire fenced run for him, with a roof? It would keep the dogs out, for one, and give him some fresh air.
Hope all is well!
Elly n’ the dawgs