So there is this dog that keeps coming into our yard...?

are you asking a question or telling a story? I guess if her privates are swollen then she is most likely in heat. In this state the dog will do all she can to find a mate. Its a drive that a female will have. She is playing with your female to release fustrations. Dogs are quiet excitable at this time in there lives. I am sure she had just recently escaped her fence and decided to let off steam with your dog before crusing the neighborhood to look for boys. If her tag is wrong you should let the owners know so it will be eaiser for others to find her home for her.