but by the op sending her dp and dd to his parents over Christmas she is sending out the message that she doesn't want anything to do with them.
It is the op who is then sending out the message that they are not a united front on this. And once you do this once how do you come back from it? And what do you tell the children - maybe the op's dd is only young but one day she will be older and will want to know why mummy doesn't go to see granny and Grandad.
One of you has to be the bigger person.
About 5 years ago me and my fil had a massive falling out. It was as a result of a row me/dh/sil/bil had about ds, and in me trying to put things right I inadvertently made things worse as Fil took the opportunity to tell me what he thought of me. Some very hurtful things were said, including that I was a bad mother and that he thought the way I was bringing up my ds was harmful to him (sahm, daring to pick up my baby when he cried ). Following the row I was naturally very upset, and initially I said that I didn't want anything to do with them. However they are dh's parents and they are ds' grandparents, and I wasn't going to throw my toys out of the pram and sulk, and i refused to leave my own home if they came to visit.
After that row fil didn't speak to me for two years. Literally. He would come to my house and wouldn't speak to me (and they would be staying over night). But I still never stooped to his level - I went out of my way to be hospitable as always - one of us had to be the adult and it certainly wasn't him.
The row has never since been brought up, but it just happened that he started talking to me again, whether that be because he realized he wasn't achieving anything or whether mil told him to get a grip I don't know. But we are all on good terms again, and although deep down I don't think he nhinks the world of me I think he probably has more respect for me now because I didn't use the row to create a family rift between him and my dh/ds (and I could easily have done).
Unless someone is blatantly evil, (and tbh I think a disagreement over religion isn't intentional nastyness, it's just a strong difference in views), I think that people should make the effort to get on especially where you share a family member, ie dh/dc.