Stick to your guns on the anti bark collar. It'll just make your dog fearful.
My dog is a very barky breed but I've got her to the stage now where I can say 'enough' and she'll stop - mostly. The trouble is, we might not like to hear it, but it's normal dog behaviour so needs to be really worked on.
If someone comes to the door she gets excited and barks, but I won't open the door until she stops. She gives a couple of nice gentle barks if she wants to go into the garden and that's fine. She does have a bit of a bark when she sees or hears someone outside but she stops when told. So I'm happy with all that.
I found that when she was barking for whatever reason, if I could manage to get her attention on me, say the signal, in my case that was saying 'enough' and then reward her with a treat the moment she was quiet, she soon got the idea.
I had to work at it non stop and did it every time she barked when I didn't want her to but it worked in the end. We did get through quite a lot of treats - obviously she doesn't get treats for it now - but I'd just cut them up very small or if your dog is on dry food just use up some of his dinner.
You can teach a dog almost anything if you stick at it and reward them enough.
Not sure about the cats. I had two very old cats when I got my dog, one of them ignored her pretty much and the old tom used to watch her play and would curl up and sleep with her. If they seem to enjoy the play I'd let them get on with it but keep a careful eye on them to make sure there's not too much scratching or biting. Sounds like they're having fun.