My Mom hated cats, stemming from an incident in her youth. Sensing that hatred my cat Cleo just fawned over my Mom. She'd rub on her, and sit next to her when she was visiting. She didn't do that with any other human!
Mom had a particularly close relationship with my Springer Fatty. I swear she could tell him something in English and he did it, what ever it was.
It's sad about your family allergies. Animals have been such an integral part of my life that I can't imagine enforced separation from them.