Absolutely! Children should have the benefit of being surrounded by ALL family on Christmas. Unless one of the parents is an abuser and there is real reason to keep them apart. Parents, regardless of what happens between them, owe the best to the CHILDREN first.
If it's possible, then yes. I used to do that with my daughters father (and sometimes his family too) and it was wonderful for both of us to be there. My son's father it's not possible to do it with and it's sad for myself, my daughter and my son. If you can handle it, do it!
I've been sharing Christmas with my son and his mother. We have it set up as every other Christmas. If one had him one year the other will have him next year, but not New Years. If one has him on Christmas they won't have him for New Years the other one will. This does two things. It allows the parent having them to plan something. Say yours or the other parents family lives out if town and you'd like to go home for Christmas, it will allow you to set up the time. And second, the other parent still has time to celebrate Christmas, after, before school starts up again.
My parents are divorced and honestly, it's made me hate christmas. There's always a one sided competition. My mother always wants more time with us on the holidays, and my dad has to fight for anything near equal hours. Then there's the hassle of going place to place. There isn't any time for...Christmas-y things anymore. No cookies, no carols, no christmas movies. It's just not a fun day anymore. If you can do anything to prevent this for your children, I would advise that you do it.
Yeah I was totally fine with it when I was younger. I would spend Christmas eve at my dads then he would drive to my moms house so I could go back home. Now my father has gotten quite pathetic since my grandmother died a two years ago and my dad had problems and whatever. This year he's spending Christmas with us and staying at my other grandmothers house. I don't like it anymore like I don't like seeing him on my birthday or on Christmas or anytime actually which is pretty sad. But I guess it's fine I don't know.