I understand that must be upsetting, and it may be that your mother is just playing favorites. Other possibilities:
Is it possible that this is an age thing? I mean, 2 1/2 year olds 'get' Christmas and like gifts, 1 year olds don't really care. (And you can't really judge by what she gave the oldest when she was 1, either, because you always overdo it with the first child on gifts, toys, etc!).
Is it possible that she is trying to make sure that your older child feels really special and has lots of goodies to recognize that she has had to make a big adjustment with a new baby around and is sharing Christmas for the first time with a sib?
If you really think that she is just playing favorites then it is imperative that you tell your mother, 'we need to have them receive the same number of gifts- I don't want any reason for them to feel hostile or competative with each other.' If that means less gifts for both, cool.
Because, you know, their relationship to each other is primary- they will be alone together in the world someday when all the older family is gone and they need to have good, happy memories of holidays and childhoods where they felt equally valued.