I want to ask my babysitter to change their vacation plans
Why do you wan your babysitter to change their plans?
I want to have them closer to me if I need them for an emergency.
Babysitters need vacation time too. You should not be selfish and let them enjoy their temporary vacation. Think of their needs.
I want to be selfish and they work for me, not the other way around. They should be available when I need them.
I understand that you might need someone to watch your kids in an emergency, but you will have to find someone else while your regular sitter is away. It is not fair to them to have to stay close by just so that you are not inconvenienced.