I don't send money with my kids for vacations with her dad
Why don't you send money so that your kid can have fun with her dad?
I don't believe him and I see him as dishonest and cruel person.
It is understandable to not want to give money to her dad when you don't trust him, and he should pay for it since it is his kid too. It would be a good lesson for him.
He's not trustworthy and could be using the money to pay off some debts.
I get he should be the one paying but it might be good to give her a bit of spending money. Maybe you should talk to him if he has trouble with debts, vacation would not be the best thing to do.