Man - those birthdays around Christmas are hard!
My youngest has a birthday 10 days before Christmas; my Mom's birthday is 4 days before Christmas and my Grandma's birthday is 3 days after Christmas!!
For daughter, we refuse to decorate inside the house until we've had her birthday. We may decorate the night of her birthday, but only after we've "done" the birthday thing. Not so easy for you all to do.
For Mom and Grandma well, that's harder. Here are my suggestions:
First - a first birthday IS about the family more than the kid. Make it small and take TONS of pictures.
After the first, think about these things. I know that it's hard to manage birthday and Christmas so close together. But my Mom said when she was a kid she got either Christmas presents or birthday presents. Don't do that. Also, (this isn't as easy as you think!) plan ahead. Birthday wrap is VERY hard to find around Christmas - so plan ahead for that. My Mom used to get upset when she got her birthday present wrapped in Christmas wrap. So, if I can't find something, I turn the Christmas wrap over and let the kids go at it with crayons. Anything so it's not Christmas.
I know those don't really help you this year. Just try to make sure that whatever you do for birthday doesn't have Christmas tones to it. (No green and red cakes!)
Those are the suggestions I have, hope they help some!