£1200 for one week in summer is not extreme, depending on the size of the property and it's amenities.
And it is, generally, unfair to commit to something and then back out further down the line.
Having said that, £1200 is for the accommodation only, it doesn't include travel there and back, food and activities. That could potentially bring it up to nearer £2K depending on what you were doing.
A trip to the zoo for example, is probably going to be £50 in entrance fees for one adult and a child, and if DS knows OP's kids will be allowed ice creams, snacks and a trip to the gift shop then that's extra she will have to factor in.
OP, I can see that you would be annoyed/disappointed that she has backed out, but your post implies you were booking anyway for your family, you would have booked even if she had said no at the start.
Your kids are disappointed that their cousin isn't going now, but it's probably 3 or 4 months away, they will have got used to it by then, it's not like she backed out on the day you travelled.
Unfortunately your posts are coming across like you are used to things happening the way you think they ought to. Perhaps this is another reason she doesn't want to come. She is effectively joining you on your holiday so will not have any input into activities or costs, and can't say "no" on the day, as she will be disappointing your kids.
Just accept gracefully that she isn't coming and has good reasons for not doing so, which might be financial or they might not.