Your story is beautiful; made me cry. I've had dogs all my life and they give so much and only ask for love in return.
Rabbit's behavior is not unusual. Cats and dogs have so much love to give and they know just what you need when you are sad. Get another cat. You obviously took excellent care of all your cats; I can't imagine why a shelter would turn you down. There are lots of rescues and shelters. Don't give up. Try Pet finder online. Good luck!