forget the dogs - the real issue is...........rent to own is not a good idea, in general, as it strongly favors the owner/seller.
Most sellers who want to sell and can sell, sell now, not later.
You will be expected to give an upfront NON-REFUNDABLE deposit, and pay rent over and above the normal rent.
Only that extra rent will be applied to the purchase, but it will also be lost if you do not buy the home for ANY reason.
So, if you do not qualify for a loan now, you better be sure you will qualify at the end of the lease or risk losing your money.
My advice is to rent while working on whatever it is that is keeping you from buying a home in the normal manner. Buy when you're financially ready to do so.....another plus will be that you will have a full selection of homes from which to choose.
Rent to own is not a good idea with or without dogs!