I'm not going to allow my children to use their phones to contact my ex
Why aren't your kids allowed to see your ex?
I want my kids to behave well and I want to take care of them.
I can understand that you might have issues with your ex, but it is cruel and wrong to prevent your kids from contacting one of their parents. You should discuss the issue with them and perhaps set some boundaries, but you cannot cut your ex out of their life, even for noble reasons. Otherwise they might resent you in the future and decide they want to cut you out.
I'm not just doing it for noble reasons, I just want to punish my ex after she sent a picture of her vagina to my business partner.
Despite all her flaws, don't you have to have a healthy relationship between the kids and her? The kids aren't involved with her misdeeds, so they still deserve to have a happy life with her.