Can I do a joint custody agreement for my dog with my sister? I am the financial caregiver providing shelter, food, vet fees.

Atty Langer is exactly correct that it would be very unusual for a commercial creditor to have any interest in levying against pets or other personal effects. He is also correct that it would be prudent to consult with counsel about the lawsuit and you may be able to obtain assistance and guidance with the lawsuit from your local Legal Aid organization.