What should have I done?

No.
1. It's not your car.
2. Your mom lent it you you and no one else, not even your husband.
3. Tell them you can't do it. Plain and simple.
4. You can't do anything about their feelings. They choose to feel hurt.
5. Besides, your husband should really take care of the problem. They are his parents.

Your family is a bunch of manipulating idiots.

You said NO.  That is that. Tell them to piss off.  Seriously. They don't care about you and your word to your mom? Tell them to stuff it. 

Thank you, Marguerite. I needed to hear that.

It really didn't feel right to let them use it without letting my Mom know. Thanks, Sharonna.

No. You should not loan a car that is not yours.

Just tell them that. If they insist on wanting to borrow it, explain that they must ask your Mom first.

I mean what happens if they borrow it with out permission and it gets wrecked. That would really create hard feelings all the way around.

I agree with the other responses. It wasn't yours to lend out. If it was me, I'd be ticked that you lent my car to someone else when I was entrusting you with it. How would they feel if the shoe was on the other foot? What if it was something of theirs being lent to your mom? I know some people are ok with that, but wit something like a car? Nun uh. You were in the right.

I agree with you .. is not yours to lend .. I would have handled it a little bit different though. .. rather than getting then Rio ask I would have asked mom. .. When she said no then that's what you tell them ... It can be difficultly but you did the right thing :)

No, do not loan your mother's car out..  Give your mother her car back.   Get yourself your own car.  You are a married woman;; time to adult.

Nope your not the bad guy here.. You have dealt with the situation in the correct manor..

Well done...

exactly what you just did, telling them to ask your mom

Thanks for the comment everyone.