Legal Question in Family Law in Texas

There's not a real time limit for this (I assume that you didn't leave the pets with him six years ago).

Write him a letter - PAPER letter - no phone calls, text messages, or emails! - and politely tell him that you're ready to come get Fluffy, and tell him when you're coming over with the carrying cage. Thank him for taking care of the animal. And then, at the appointed time, go over there with a carrying cage (and a couple of friends).

If he doesn't give you the animal, you have to sue him for conversion, and it will be a "swearing match" in court.