Yes, you should do your best to stop it now. Probably won't work, but you should try. Limit your interactions with her as much as possible if she continues to make these 'jokes'. If she really dislikes SeriousCat, she won't change.
Since she seems to be scared of him, maybe HE could tell her to knock it off? "Mom, MerryCat tells me that you are hurting her feelings but disguising your criticism as 'jokes'. We want it to stop."
I was in a similar relationship
with my MIL. She disliked me for no reason that anyone else in the family could see. The best I can come up with was that we married without asking her permission. She didn't even try to hide behind PA 'jokes', but was just generally very cold and hypercritical of me and my kids. DH and his family just shrugged it off as 'that's just the way Mom is.'
IMHO, "that's just the way she is" is NEVER an acceptable response to one family member abusing another, and this is abuse, just as much as making outright hurtful comments.