How do I convince him???

How do I convince my husband to get rid of his dog? It's his old family dog that we have had for a year because his mom moved away. She is coming back next year so I want to talk him into either making her keep the dog or rehoming him completely. It's not that I don't love the poor thing, but I am allergic to him. My dog as well. My dog just makes me itch sometimes because she is pretty much hairless and that's why I got her. His dog has very long thick fur and it makes me break out in hives, sneeze, itch, and sometimes I struggle to breath if it gets in my face. It's only getting worse as well. I told him if my girl has to go as well then so be it, but I'm miserable. He loves the dog and so do I, but my health is more important and he just refuses. I even asked if we could shave him to see if that helps and he won't do that either. It's to the point where I am even thinking of moving out and into my own place because I can't stand being home. Please help me because I really don't want to do that.

*Forgot to add that I've tried allergy medication and it doesn't help much at all. I am allergic to benadryl. I really just want his mom to take him because he was hers to start with. She just left him when she moved away.