In a word, no. Although spouses often view themselves as “pet parents” of their pets, divorce law does not (currently) equate pets with children in any way, shape or form.
Quite the contrary, the law casts pets as property. A fair market value is assigned to the pet.
Like any other asset or debt, the pet is assigned to one spouse and some other similarly valued asset is assigned to the other spouse.
The choice of “assignee” (recipient) may be enlightened by consideration of the pet’s needs and which spouse has already demonstrated that they are better equipped to meet them. Or the ruling may be fairly arbitrary.
So what’s a pet lover to do?
The Law is what controls in divorce court, and the matter is before the divorce court because the spouses can’t agree upon a resolution.
But The Law may not produce a result that is in the pet’s best interests, if the spouses care about that.
Alternatively, the spouses can reach their own agreement as to which spouse keeps the pet full-time, they can agree to some sort of timesharing or visitation schedule, the spouses can agree to rotate physical custody, or the parties can agree to designate someone else (like a mediator or arbitrator, a trusted mutual friend or relative or, for that matter, the pet’s veterinarian or groomer) to choose the superior pet caregiver.
In general, animals are less adaptable than people (or children) and crave routine, structure and a stable territory they can make home.