I could see inviting an ex spouse to Christmas, but only if the kids are close to said ex spouse AND the co-parenting relationship has been friendly, at the very least. This is not the case here.A few questions.
How old are your kids? I have three kids, they are 16y/o.
Do they live with her and they spend school breaks with you? We are supposed to alternate weeks and holidays but they are with me most of the time. I think their mother calls or texts them sometimes but they don't see her much.
What reason do your kids give for not wanting to spend it with her? Their relationship with their mother suffered during the divorce. I am guilty of putting the kids in the middle and telling them things that I shouldn't have. I realized that recently and I do feel guilty about it.
How is your co-parenting relationship? We used to fight a lot but now we have very little contact and no longer fight. Any contact we do have is about the kids and very business-like and disagreements are handled without fighting.
How do her and your current wife get along (if they interact)? They don't interact anymore. Early in the divorce process my ex-wife was not very friendly or easy to work with but that has stopped. If we have to be at the same event I avoid sitting or standing near my ex-wife and she seems to do the same. I was with my ex-wife for 27 years and I think that is a bit intimidating to my wife when we've only been together for 6 years.
Your ex wife is mother in name only as she seems to rarely see or interact with the kids at all.
The kids are well old enough that if they wanted her there they'd ask and you haven't indicated they've asked.
You and your wife are not close, friendly, co-parents.
I can't see a single reason to invite her unless it's solely to ease your conscience. That said, if your ex was the cause of the divorce through infidelity and you told your children that, I can't say I see why you'd have any reason to feel guilty at all. In an infidelity situation, I feel the kids have a right to know who nuked their family and the adulterous spouse can just take their lumps as part of the natural consequences of their actions. So, if that's what you feel guilty about, don't.
Your current wife already said no. Unless there is a cordial relationship between the former spouse and the current spouse, best side with the current spouse lest she also become an ex. I dearly love my DH and we've been together 20 years. If he asked to invite his ex for Christmas, I'd say a firm " NO!". If he pushed it by asking again, I'd pack up his stuff, put a bow around his neck, and call UPS to deliver him to her.