OP this absolutes stinks. You are quite right to feel aggrieved, and it is not for you to cover for these two people simply because they can't be bothered to get child care they have had a whole year to sort out. It is very poor management from your boss that this is happening.
I don't think you mention whether they are single parents or not, but to my mind that is irrelevant, because even if they are they shouldn't have taken a job which means they can't fulfill the rotas they are contracted to do. Plus if its part of the job that management can simply cancel with some notice annual leave to ensure cover, then I'm guessing they took or have kept the job knowing that, and would have some sort of back up for those situations, as they could be in that position at any time during the year, not just Christmas.
I'm a mum with two children and when I went back to work I only took a job that worked around child care either my hubby could do or that I paid for (& occasionally I could ask friends for help). I did not look to do a job which meant that I needed to get my work colleagues to do extra cover for me to their detriment. So if I had been a single parent I would not have taken a job where I might have to work days it wouldn't be possible to get child care. And I find it really strange if they are in that situation that other members of their families such as grand parents could not help them out. Yes as some pp here have said, they might be totally alone and have no-one to ask, but then if so, they are they are in the wrong job.
I now work doing a job which is potentially 365 days a year. And it does mean I can be working weekends, bank holidays and certainly Christmas Eve/Day, Boxing Day and New Year. And, I am Christian - so the actual day for our family is important for something other than just a big blow out family meal and unwrapping tons of presents, because to us it has religious importance. But that still doesn't mean that I will not take my fair share of working Christmas Day. In fact I have done that many times, and gone home and cooked Christmas Dinner and done the whole Christmas thing.
What is quite ridiculous is for the OP to be bullied in this way by her colleagues with children who are refusing to work and by her manager to not deal with this situation. It is the two people who are now claiming that after a year's notice they cant get child care and therefore can't fulfill the job they are contracted to do, that are taking the proverbial.
I had this problem with the first job I had after the children when the people in our office changed (though not with Christmas or New Year as with that particular job we didn't work them). It was a small office 2 deputies - myself and a colleague supposedly equal with me, and a manager who the other colleague became extremely friendly with. We both had primary aged children although I think my two were abit older than hers. I either used my hubby or my child minder to cover holiday time or if the children were sick.
I like to think I'm a reasonably fair person, willing to take turns with others and considerate with supporting work colleagues. I even worked from home laid up on the sofa (unable to drive) during 2 weeks scheduled sick leave following a knee operation as my manager's mum had suddenly died.
The first year we all shared an office I offered to work flexibly most of the summer holidays and December up to Christmas as we weren't taking a holiday that year so my colleague could just pick what she wanted. She booked the October half term as going abroad. She booked the following February half term saying she was going abroad - but then didn't go. Thinking I just wasn't being organised enough I asked about taking the next half term as I wanted some time with my kids when they were off school. I even said to her, if you want to agree which half terms you want off we can alternate it. She had already got something booked that half term so I said I'd take October instead. Summer holidays weren't a problem, again we weren't going away so I just tied in with her and my boss's plans. We were hoping to go away the following February to California for 2 weeks. So I spoke to my boss early about it to avoid any problems and she agreed I could go.
Two weeks before October half term - suddenly my colleague had things booked and needed the time off and went ballistic at me saying she needed time off because she needed time with her children and I didn't need it because I had a husband and child care. She also had a major melt down shouting and screaming, about me having 2 weeks in February (which would have included half term) because she was planning on going to Australia and that was the best time for her to go.
She was also often quite abusive to me in the office when the manager wasn't there (which due to part time rotas and the type of work we were doing was quite often), or used my ideas and took credit for them with management.
By end of January I wasn't working there anymore, although not directly because of her - significant family illness. But I have to say that if it hadn't been for that I think I would well have left anyway as my colleague was very entitled, had the manager wrapped around her little finger and knew exactly how to suck up to those higher up to get her own way - I'm just not office politics savvy enough - I just want to do my job well.
I don't think people should get priority for annual leave just because they have children. I'm sure if I had been single my old colleague would have used it left right and centre to get her own way and said she needed that time because she had children so should get priority.
People like her and the OP's two colleagues simply want their own way all the time. It could be annual leave, leaving early or last minute time off for appointments (I forgot how many times I was asked to cover for her during my days off in my old job because my colleague needed to take DCs to dentist etc etc) - whatever it is, the real crux is that people like that believe they are more important than anyone else and therefore are more deserving. They are only interested in how to use other people to get their own way..
If it wasn't to do with their children, I would bet there would be something else they would claim why they needed to take Christmas off again. There would be something else that would mean they wanted priority. Its quite simple - its called being selfish.
I really hope you get this sorted out OP.