I think you are being put in a very unreasonable position. He should be the adult here and realise that his plan is actually not going to work this time. You and your sister sound like you bend over backwards to make his life as good as you can and actually you are BOTH allowed to set some boundaries.
From what you have said, he probably just doesn't think through the implications of bunking in on an already planned trip. He thinks of himself as a young, fun Dad who usually goes on holiday with his daughter and enjoys it.
He probably doesn't really realise that she needs a break. In a way that shows how lovely your sister is because she hasn't let on to him what she really feels like!
In his head, he has come up with a brilliant way of enjoying his usual holiday company AND seeing you guys.
What he isn't thinking through is that this hasn't been planned as a family holiday. This is two mates meeting two other mates who happen to be related.
It doesn't even sound like this holiday is one where YOU will get to spend lots of time socialising with your sis, dh and friend. You will be home with the baby!
He hasn't been recently widowed. He is not infirm and lonely. He is a sociable guys with a job, friends and an active social life who just fancies this version of Xmas over his previous plans. That's absolutely fine and I can totally see how it has come about.
However, to make his idea happens means creating unnecessary stress and presssure on you, your DH, his friend, your sister AND your child. That is silly.
You and your sister need to present a united front and (kindly) tell him it isn't happening. He will be disappointed but that isn't your fault or responsibility.
Yes, Christmas is about family and compromise but I think some posters on here have been really unfair on you. This is a particular moment in time with particular circumstances and it JUST DOESN'T WORK!! Oh, and he won't arrive until Boxing Day anyway WHICH MEANS HE DOESN'T SPEND XMAS WITH YOU ANYWAY!!!!
If you just can't bear to say no then definitely definitely definitely say he can only come for half the time. Give them a week on their own and a week of him bunking in with you. He can choose which week if no-one minds compromising on that.
What does he best respond to - the truth? a tug on the heartstrings re giving your sister some time out? a white lie about trying to set up a romance? tears because you are so worried it is all too much? begging? telling a straight no and getting a row out of the way? Whatever it is, it has to come from you all and it has to be done soon.
I really feel for you.
The perils of living in a faraway place that everyone wants to visit!