Cat stalking other cat, causing severe anxiety

I have two cats, one male and one female. Both are about 10 years old and both have been in the same household for about the same time. My male cat has progressively become more aggressive towards the female. He "hunts" the other cat, stalking her around the house and occasionally pouncing on her. His idea of playing is not the same as hers. She is large and able to defend herself mostly but she's not aggressive enough to really fight back. In fact, she cowers, runs, and stays on my bed (her safe place). It has gotten to the point that she has been defecating on my bed. This morning, the male cat cornered her bad enough that she jumped on the bed and peed all over my husband's head and pillow. Yes, very nice awakening at 6 in the morning. We rescued a dog about a year ago. Since then, the cats' personalities have not changed. However, the male cat has intensified. It's as if he is asserting his alpha male dominance. We try to give him extra attention but if we are around with the other cat or dog, he just stares at us from across the room. You can see the jealousy all over his face. Interestingly, the female cat has no qualms about slapping the dog a couple of times in the face if she comes within 6 inches of her. The dog is very aware of this and steers clear of her space. Aside from the stalking, the cats get along fine and always have. There have been times the male cat has come to her rescue when she has cried out in pain or stuck in a closet by accident. Any advice on how to stop the stalking, how to make the male cat less jealous, and for the love of God how to help prevent the peeing and defecating on our bed and allowing the female cat to feel safe in her own environment???