Thanks for the question. If you are planning on buying this is a non-issue. If you are planning on renting, it becomes more difficult. It will depend on the type and size of dog and on exactly where the house is located. If in a community with a HOA, it becomes more difficult. Please contact me with your basic parameters and I will be happy to help in your search. Happy New Year!
Having a Realtor represent you increase your chances of being accepted. Also offer an amount a little above fair security deposit for the dog in all your offers. This shows you are less likely to allow your dog to harm the property and will protect the landlords property value if you are unable to control your pet. This will also increse your chances of success. If you decide to move closer to Pittsburgh I will be happy to help you.
I would suggest hiring a Realtor to locate your family home that accepts dogs. There is a lot of work that needs to go into finding this type of housing. You need to be specific and direct with whomsoever you decide to work with in finding you new home.