I am not an expert on Beagles but I do however know what you are going through. We had a beagle as well that would do the exact same thing only difference was when we took her for walks she would be better. I think in Giddy's case(my beagle) that she was bored maybe and resorted to peeing and pooing in the house to either 1. get back at us for not entertaining her, or 2. she was bored and had nothing better to do. She will still have her odd accident if we don't take her out for walk but she is much better. I don't know what to tell you but that was an idea that did work for me. Good luck and hope you find a solution to this problem. Dogs are so loveable and its a shame when they can't train properly and end up causing us stress. Good luck again!