I don't get along with my mother-in-law and because of that my husband always feels I don't care about his family. What should I do?

Not being capable of getting along with someone and caring about someone are two different entities though co-existant. You can demonstrate your feelings in many ways. Be sure to isolate the issue of not being allowed or able to peacefully co-exist with someone from the fact that despite everything else there is empathy and love.

First, you need to talk to him and explain the situation. It's not a matter of not caring, it's a matter of butting heads with your mother-in-law. The second part is examining why you don't get along with her - do you butt heads on little things, or is there something deeper there that you need to address? If it's just that you don't see eye to eye on certain topics (politics, religion), avoid talking about those topics with her, and find things you do share - perhaps a love of gardening or reading. Find something you have in common, and your relationship will likely improve. As well, your husband may be able to help you two connect. He knows what she loves, and he knows what you love - he may be able to make suggestions as to what you two can do to help your relationship improve.