Firstly, the OP has talked only in terms of Christmas dinner - nothing to suggest a 'compulsory vegetarian day'. Secondly, the OP has offered nothing to suggest that any of her guests have objected to the menu. Some people are assuming that because the mother wants to bring chicken, she is objecting to the menu No evidence so far that that is the case
And no evidence to the contrary, either. From the OP's opening post, she has categorically stated she does not want chicken at her table. This suggests to me that the vegetarian meal is compulsory, unless it is only chicken that is the objectionable item. I wonder if the Mum could take along a slice of beef/lamb/turkey. I'm guessing the reaction would be the same if the Mum suggested this. It seems we'll never know for certain, as the OP has scarpered.
We often have get-togethers with friends. We all take pre-prepared dishes to each others' homes, especially if someone may have a dietary requirement (no, I know meat is not a dietary requirement, but in this particular case it is a preference for a family member for a special-occasion lunch). It also eases the burden of the host having to do all of the work. Taking along a contribution to an occasion is perfectly normal (in my circle of friends, anyway). Cultural differences and allergies notwithstanding (I also wouldn't take a bacon sandwich to the house of a Jewish friend, nor a beef casserole to the house of a Hindu friend, for instance, that's a bit of an infantile comparison), but in this particular case the vegetarianism appears to be a personal choice, neither cultural nor one associated with allergies (from what I can glean).
There is another thread going at the moment (haven't joined in and have lost it now, as MN website has been playing up a bit today), where a meat-eating Christmas host is wondering whether the vegetable options will be adequate or suitable for her vegetarian guest(s). Her suggestions sound delicious, and I'd personally be happy with all the vegetable dishes for that lunch, even without any meat.
It is all about making an invited guest feel welcome, as many others have said before.