Although I agree with everyone else that you shouldn't have to give up your kitty, if your FI is going to continue to treat the cat this badly, it would probably be better off in a loving home. Not a good sign the cat is happy if it's living in your basement.
Make sure if you put an ad anywhere, you don't list it as "free" or "free to good home". I had to give up my bunnies a long time ago and was told by the humane society to never do that. You want someone to adopt them that cares enough to pay.
I also think regardless of what you decide to do, your FI needs a large kick in the ass! This is not how you treat animals, the woman you love, or handle a situation you don't agree with. He knows you want kids and is holding it over your head. Sounds like he has control issues. Don't start off a marriage like that. He needs to understand how to respect you and animals.
Sorry you are going through this. I can tell how much you love your kitty. Your kitty needs you to be it's voice and stick up for it. When you adopt an animal that's the responsibility you take. Good luck.