I think - deep breath - that because Christmas is such an emotionally charged and iconic family time, that it probably would make things (even) worse if she was banned from yours at that time. That's not to say however, that I don't sympathise immensely (having had to put up with similar hurtful insolence in my family, though thankfully not directed at me) and I do understand how you must dread what should be a special time spoilt by a horrid atmosphere.
However, notwithstanding the fact she's a "typical teenager" and that such behaviour isn't uncommon, I do think she should be disciplined when it occurs .... in exactly the same way as you'd discipline teenage children of your own. Being a certain age may make such behaviour more likely, but it doesn't make it right does it ? Suitable punishments obviously need to be worked out between you and DH, but teenager or not she needs to learn that there are consequences for being rude and nasty - even if it is Christmas ! You may find that in typical teenage drama queen style she may decline to come over anyway, in which case problem solved (for now) but unfortunately, I think this is one of those situations where you're damned if you do and damned if you don't. If DH maintains she's not invited, you will no doubt get the blame for this as she's likely to tell other people how you've "pushed her out" and turned her dad "against her". The fact she's being completely hypocritical about it - slagging you off one minute, but still expecting to be welcomed with open arms - won't, unfortunately, cross the minds of many self centred teenagers.
To avoid that, I think you have to try and occupy the moral high ground and invite her even if it's through gritted teeth and you have to put on an Oscar winning performance when and if she arrives. There is of course a slim possibility that she might just get the Christmas spirit and behave decently anyway, but if she doesn't, like I said, any bad behaviour needs to be nipped in the bud straight away. Honestly - if she started, I'd want my DH to send her to her room and tell her that she could think about how hurtful she'd been while she's up there. If she started to argue back, he could tell her that he wasn't prepared to have his Christmas - and everyone else's - ruined any further, and that he'd speak to her tomorrow when she'd had time to reflect. That may sound harsh, and it might be for an isolated bit of "typical" teenage rudeness, but I don't think it is when this has become a regular occurence.
I really don't envy your position at all, and it's such a shame this has blown up comparatively recently when you've been in each other's lives for so long. Not that it justifies it, but is there anything else going on in her life which is worrying/upsetting her and causing her to take it out on you ?