The foal or colt might be an inbred, but if raised smartly, it won't be an issue. The only issue left was your mother herself. How will you deal with the dog thing. Then, it came to you. Just don't bring it up. And, if you need to inseminate her, just remind her of the father. Doggy humping in no time. Its all a system with a bit of care and work can succeed. She won't even know that its hers and the inbred won't know either. 