The kids will learn to feel anxious because of underlying anxiety between parents at Christmas if he gets his way so do everything you can to teach your babies resilience and that they can depend on you to provide a wonderful fun Christmas, no matter what confusing or annoying shit their father dishes out.
You are doing great as a young Mum , keep contacting Women’s Aid for advice when he causes conflict. Such a game playing arsehole he sounds. it is so hard that he is distancing himself from the family, refuses cm then demands more time.
So difficult for your tiny little boys to see/feel the parent conflict, but great you are getting good advice and dealing with it firmly but fairly.
I feel bad for you that he is making it so hard for you and causing such stress for you.
It is really annoying that their father is such an arsehole about demanding more time just to save money, when in the past he has been happy to leave most of the parenting up to you, and additionally is cheating his own children out of child maintenance payments.
In the end you can’t change him but you can focus on changing what your kids see of you in reaction to his BS.
I think your kids would love to feel that you are happy for them to celebrate the festivities twice, as @Lockdownwaistline suggests , and while you can’t change their Father you can change how you react to him and you can change how much it impacts them.
The kids will love going through the rituals before they go to Dads for Christmas, too, so you can enjoy focusing on the Christmas lead- up rituals too, such as leaving out oatmeal and carrots for reindeers, putting on a few favourite Christmas songs and teaching the kids to sing and dance while wrapping a present for their family. You can enjoy age appropriate games , craft, etc in the lead up to Christmas just the same and then hopefully they will love sharing festive celebrations with you, no matter what day you share it on each year.