Idk, man. My mom died and I don't understand 'your mom' jokes at all. I actually become very irritated if people mention their own mums let alone if they joke about my mom or moms in general. You never know how sensitive someone can be with their parents or what experiences they may have. You might have hit a weak spot.

I'd suggest that you give her a bit of time, apologize again and express how much you want to be friends and promise you'll never act like that again. But really do so if she forgives you.