YANBU at all to feel Lonely at christmas time, but as you keep on insisting your dd must go to her dads to see his family then i think your half to blame if im honest. No way would i let ds go to his dads every single christmas if we were to split up. I dont know many people who would allow that to be honest.
You say you have no close family and dh works, fair enough, but you have 2 children now. Christmas makes me happier when i focus on the children in our family which is what its all about, giving them a lovely day gets me through it. Wouldnt you love to wake up on christmas morning and see your 2 children playing together with their toys. Have you thought about the fact your dd will grow up having no memories of her christmases with you. That would be unbearable for me.
I dont mean to come across as harsh op, i really dont, i just want to drum it into you that your ex is being really unfair to have every single christmas with your dd, maybe he has new faily and kids whatever, your still her mum. He can always see her at new year and if that doesnt fit in with his new families plans then tough!!! Your in her life so stand up for yourself, tell him he can have her next year as you'd like to have your own family christmas with your dh and her sibling and this is how its going to be from now on. I was brought up by divorced parents, they swapped every year. If id of only had xmas with 1 id feel a resentful to that parent if im honest for not sharing me.
All my single parent friends do this, 1 will have kids at christmas, 1 will have them at new year, ten they swap next year, nobody misses out. If you dont do this now then this is how it will be for years to come, imagine in 10 years still feeling this way and never having spent a christmas day with your own daughter. As someone else said upthread no court in the land would agree to that, and im sorry but it baffles me that you think its ok?? Please op start making you own christmas with your children, give them some lovely memories of you!