First off, take a deep breath. In fact, take four or five. Relax. There.

Okay. This is what I get from your post:

1. You really want to go home for Thanksgiving.
2. You want to stay with your boyfriend, not with your parents.
3. You are worried about your car making the trip.

It seems to me that you need to know one thing: whether or not your car is road-worthy. Once you know that, the rest is pretty clear.

If your car is not safe to drive 1300+ miles in the next 10 days, then you have a couple of options. Rent a car: you say you cannot afford it, so can your parents and/or boyfriend chip in? If so, rent a car. If not, what about other transportation options: train? bus? flight? Any of those possible (with financial assistance from your family and/or boyfriend)?

If your car is safe, and you feel confident that you can make that drive safely, then it seems like you have already answered the other questions.

The sticky point, it seems, is getting up the courage to tell your mother that you will be staying with your boyfriend. Your reasons are very valid and you should just be honest. You are staying at your boyfriend's because that is the arrangement that works best for you. Be prepared for push-back from her--most mothers do that. Just hold your ground and politely restate your position and end the conversation with something like, "I'm really looking forward to spending Thanksgiving with everybody. See you in a few days."

From your post, it seems like staying at your parents house is just simply not an option. It is not what you want to do, so don't do it.

Do what makes you happy. Period. At Thanksgiving and in life.