I'm annoyed that a close friend asked me if I would be willing to look after her kids.
Why is her asking that annoying?
I'm too busy to take care of her kids at the moment.
Since you two are close friends there's nothing wrong with her asking you for help. You should do this favor for your friend if you're able to.
She should know that I have stuff to do and I can't do this. Also she was trying to make the kids cry so they would be more willing to spend more time with me.
It's good to do a favor for your friends. But if you can't you can't. Just say no this time and make it up to her later.