You can get custody of minor children in a divorce but not a pet in Maryland, DC and Virginia and most other states. The law views pets as personal property, with no more rights than a table, chair or lamp.
But if you live in Alaska, divorce court judges are now required to consider the well-being of the pet under a new law. The court may award custody of a pet on the basis of what is best for the animal, not the human owners.
The law also allows judges to include pets in domestic violence protection orders.