Do you think there will be a problem if I want my ex to cancel her plans to come pick up the children?
It depends on what's best for the children.
Yes, I'm sure it's best for the children.
Emergencies happen but it is not good to tell your ex to do what you want. It will cause you guys to fight. It would be better to find somebody else to take care of them when you are on your time with them.
So I can't have my way?
If you and your ex have an agreement that she'd rather be called than a babysitter, that's okay. But, If you are doing this so that your ex has to cancel her plans, that isn't good. You can't control someone and most definitely not using kids as bait.