Hi Leanne - Let me start by sharing our solution to a similar problem (however, it was my family and ME that didn't want to go! And we're all local...)
We have created a tradition that we now give our church all the money that we would have spent on gifts (over $1,000) and then we go on vacation! Ooops - we're away... Can't attend. We'll miss you! :-)
Since many of us take an annual vacation, we just take ours then and stay home over other school vacations. Problem solved.
Beyond that however, this goes well beyond holidays.
I think the crux of the problem is was simply stated in that you have made reasonable requests of these people and they have ignored them. And they don't treat you with respect. To my mind, that is the reason to stay away...
Relative to the Holidays - if you celebrate Christmas for religious reasons (you didn't say...), and these people do not - and, in fact, disrespet and denounce your faith, again, I say stay away.
I wonder what it teaches your child as she watches the way you are treated by these people?
Remember this - we teach our children who to be by who we are in the world. PERIOD. So the family that you associate with be a big infulence in who she becomes and how she relates.
So - I totally agree with you and urge you to find another time to see them... It could be as simple as Christmase Eve or sometime during Christmas week.
Please don't ever let anyone compromise your standard - or your child will too! See them at other times - and as Dr. Joy Brown says, be cheerful and stupid. Just don't "get in to it" with them. Smile. And keep quiet. Then leave when you're done.
This will also teach your child tolerance. There are all kinds of people in the world - and how blessed you are to have some of the worst in your own family! (See how God works? He has given you this wonderful provision as a teaching tool for your child. Perfect.)
And not to get into the obvious, but let's not dwell on the safety factor with a "strange" - i.e. new - very small child around the dog that doesn't sound like it's very well trained (treating a dog like a human - and not a dog - is bad training).
If you dwell on this, then they will expect things to change as the child grows up. It's not about the dog.
It's about who they choose to be and who you choose to be. So stand strong in your convictions, but practice and teach tolerance all the while.
Your child will be better for it. (And if it comes down to it, send your husband. Really. Don't make Christmas Day a breaking issue. When you think about it, it's not such a BIG deal - so don't make it one.)
See if you can find Charles Swindoll's quote about Attitude. If you can't find it, let me know and I'll send it to you. It says it all....
Good luck. Be well. You already are blessed!