How do I handle my dog s behavior towards my other dog?

Sounds like normal dog play to me. If no one is getting hurt, and no one is getting threatened, what is the problem? If the pit bull doesn't mind, why do you mind? I don't think there is anything that needs handling or correcting. You merely need to view it as not a problem. Possessive? Sure. Most dogs are possessive with toys they consider theirs at the moment. Bullying? What? The poodle is PLAYING. A lot of dogs do this "look at this great toy I have, don't you want to take it from me?" thing.

Seek professional help for yourself on how to train a dog properly since you've allowed this poor behavior to progress without proper correction.

It sounds like you have a very beautiful submissive dog (I know right the big dog that could snap the poodle in half in one bite!) It sounds as if the poodle has taken his place in the pack and that is above the boxer/bull and this is something two dogs will always do one will be above the other. I have a Labrador and he loves to carry everything but when I visit my brother and his working cocker and springador the springador will take all the toys from my labs mouth and my lab will let her, At feeding time if either of my brothers dogs move into his food bowl he backs off and lets them eat his food (of course we step in and put the dogs in their place because we own them not they own us!!) My lab is a super star perfect in every aspect he visits adults with learning disabilities, helps to teach children to cross the road and how to approach dogs but he is submissive to every other dog thats just him but its up to me as pack leader to regulate the pack.

I don`t see what the problem is.

The larger dog is not bothered by the poodles teasing and obviously does not view it as a threat.

Large dogs with stable temperaments rarely view small dogs as a rival or a threat and "will" let them get away with murder (so to speak).

If the dogs are not actually fighting over the toy then let things be.

However....If "you" are bothered by it then take all toys away and only bring them out when YOU want to interact with the dogs.

All toys should ultimately belong to the dogs leader/owner anyway.

When my old dog who was very dominant natured, was alive, my other dog used to do the same to him as your poodle does to your larger dog, but my old dog would just look in disdain as he was confident he was the top dog when it came to the crunch.

He knew if he really wanted the toy he could just take it, but he just allowed his friend to have his fun.

I try to make sure all my dogs have identical toys & chew bones. But yes on occasion this still does NOT prevent squabbles, so at THAT point the item that whose ownership is up for debate, is removed by ME (usually fussing & saying, "NO BITE") equally to ALL parties, and the "disagreement" ends.