The Community Dog
Texas law takes the position that pets are property, not family members. If you and your spouse are arguing over custody of the dog, the judge will treat Fido as just another asset. Texas is a community property state, so the court will put a price tag on him -- particularly if he's a purebred or otherwise valuable -- if you acquired him during your marriage. If you had him before you married, or if someone gave him to you as a gift or inheritance, he's your separate property and the court won't get involved. If he's treated as community property, and if you get the dog, your spouse must receive a different asset of comparable value. If you don't have sufficient assets to balance this, it's possible that the court might order that the dog be sold so you can share the proceeds. Whatever the outcome, the ruling should be included in your decree.
Custody and Visitation
Because animals are property, judges cannot address custody of or visitation with your dog. The court can't order that the "non-custodial" spouse pay support to help care for the animal. Ironically, however, the judge may decide which spouse gets the dog based on issues similar to child custody factors. These might include which of you historically cared for the dog during your marriage.