LORELAI: Because I have dibs on this time of year with you, not him! Me! And yes, he acknowledged that, and that was cool and all, but still – it stinks! Because he put me in a very difficult position because we were supposed to watch a lot of movies and make fun of Godfather 3, and the thing that I really, really hate about this is … is the idea of you not hanging out with me because you’re hanging out there with your stupid stepmother.
It is now revealed that Lorelai never told Rory that Christopher rang, inviting her to stay in Boston for a couple of days during the Christmas holidays. As is often the case with Lorelai, she’s being quite unreasonable by insisting that she has dibs on Christmas, when Lorelai has dibs on Rory every day of every year! It’s quite normal for children of separated parents to spend major holidays with the parent they don’t live with, and Christopher was only asking for a couple of days out of a school holiday break that lasts for weeks.
The real reason is that she is jealous of Sherrie, and hates the idea of Rory having another mother figure in her life. Rory quite rightly calls her out on it, and teases her about her attitude. It is not revealed at this point whether Rory does spend time with Christopher and Sherrie in her Christmas break, but it is later strongly implied that she didn’t. Knowing of Lorelai’s insecurities, it seems likely that Rory decided not to visit Christopher after all (with homework and the newspaper providing a plausible excuse, as usual).