I feel for you, as you face a challenging situation. I agree with Cindy, that you need to discuss your situation with a Landlord face to face. You will be able to work your way around it, and find a home for you and your two dogs. Be honest, mater of fact and have your facts in order, and I think you will have a good chance at finding a sympathetic Landlord.
All the best in your search.
To gain insight as to who I am, how I conduct myself and how I take great care of my clients, please refer to my recommendations on Trulia.
Neal I. Akin - Realtor
The Akin Real Estate Team
Coastal Premier Properties