If somebody asks/tells you not to do something but you go ahead and do it anyway you can't be surprised when it all gets heated. Are you fond of a fight or just the stirring part?
Why would one need to ? If the kids are living with your ex then I don't see why they'd make an issue about it. It's the kids' presents not your new partner's.
Other than that, it would be poor form to ignore a request but I don't think there's any law against it.
No, absolutely not. You would be initiating a fight. Have some respect for your ex., no doubt the children will have plenty other presents and would appreciate them more at a later date anyway.
Absolutely not. What a rat you are stirring it up at Christmas. It is over. MOVE ON he does not want you. Stop stirring it up. You get no sympathy from me Madam!
Madam? Well we are making assumptions and mine is you are male with a new woman, she has bought presents for your kids and your ex-woman doesn't want these presents in her home where presumably your kids live? Do what the ex asks, why wouldn't you?