How do you keep the pointed guilt trips from getting you down?

You tell your cousin that if she is so concerned about your mother being alone for Thanksgiving that perhaps she rearrange her holiday plans so she can be with your mother, and see what she says then.
You're right, that you need to just ignore your extended families ignorant comments, as until they have walked a mile in your shoes, they have NO right to comment.
Your health must be your number one priority, even before caring for your mother, so I hope that you will do whatever you must to keep yourself healthy and happy.
And please enjoy your Thanksgiving and don't let the nay sayers get you down.

Gently. Just say "I have some medical issues I don't really wish to share, nor to burden others with; suffice it to say I am sad about my current limitations.
As with so many others, Mom and I will be getting through the holidays the best we can, and we/I surely wish you a blessed one".
That's it. Turn their thoughtless back on them so they are able to re-examine it and learn from it should they choose to. Holidays have never been my favorite time, both from the standpoint of my view of the rest of the world outside out country, and the suffering that exists, and from the standpoint of the onus and burden it places upon us to be of "good cheer". In my next life I shall endeavor to be more like Mr. Fezziwig. Until then I will do the best I can with who I am. I wish you the best. Remember, when people are thoughtless and/or cruel it is almost never about you; it's about them. Wish them the best and move on and the epiphany of the burden lifted from your own heart is your gift.

I'd tell the cousin you're having a heart transplant on Wednesday but asked the surgeon if he'd let you out of the ICU on Thursday to have Thanksgiving turkey with mom, and he said he'd see what he could do, no promises.

Like my DH always advises in situations such as this, " Say the most ridiculous thing and leave them gaping."

First of all, it's none of your cousin's business as to why you're not going to be with your mother on Thanksgiving. You do not owe her or anyone else a reason. Nor do you need their approval.
If your cousin or anyone else in the peanut gallery I like to refer to as extended family wants to throw their two cents in, tell them to feel free to go themselves and spend Thanksgiving with your mother.
You are important too and so is your health. Too many people seem to think if someone reaches a ripe old age like your mom, that they then are the only priority in the lives of their adult kids.
They're not. If your cousin gets too mouthy and self-righteous remind her that she didn't take her own mother in even though she begged.
That should shut her up.

I guess I'm going to ask how serious are you about this? Do you want to put an end to their nasty behavior or put up with them? Have you told them what you are posting here? About all the work you've done, all the years, "down and dirty" details (spare nothing for their sensibilities) and how dare they criticize? No apologies, throw the whole unvarnished truth at them for their nasty, silly behavior? I found, by accident, that this "back in your face" response can work when nothing else will. You will not be a safe target for them - they will think twice before provoking you.

I don't know where I saw this recently (here?), but it made so much sense to me...

"If you wouldn't take their advice, then don't take their criticism."

Easier said than done but it put other's opinions in perspective for me.

Happy Thanksgiving.

Oh no, I had no intentions of her being alone on Thanksgiving, because I know how you feel and I know that you will be entertaining her this year!

Gosh Cuz, it is so nice of you to take your Aunt since my health needs to come first right now.

Love and kisses!

That's how I would deal with her if I were in your position.

I'm getting this too, even though I haven't spent Thanksgiving with my parents in over 20 years (it's my mother-in-law's favorite holiday, so we always go there, and do Christmas with my parents). My MIL didn't get to host last year and she is itching to have us there, even if it will be small because of COVID. I told the relative who lamented the idea of my Dad being alone that they were more than welcome to bring him into their home (he can't travel with us, it's a four hour drive and he's not up to it)

I'd say 'Yes, it does seem a pity. What would you suggest?'. Let cousin come up with the answers.

Or you could quote Jesus in the Gospel according to Mark, Chapter 2 verse 27: "The Sabbath was made for man, not man for the Sabbath”. There is even less justification for forcing the celebration of a secular holiday on a particular day - you and mother can have Thanksgiving whenever you want!

First of all, big hugs from me because I also have a large family and I know that the guilt trips can be brutal. I have 12 first cousins and they can be very judgmental and quick to criticize too. Anyways, if your cousin is anywhere near where your mom lives, then maybe she could have your mom over, or have Thanksgiving at your mom's house? I always find it interesting that people who want to point the finger never stop to ask themselves why they aren't doing anything to help. I mean if your mother is her aunt, then why isn't she visiting her over the holidays as well? Don't feel an ounce of guilt for taking care of yourself. I'm sure that if your mom were 100% her old self she would want you to take care of yourself, not worry about some man-made holiday season that is basically designed to make people feel bad in one way or another. If all else fails try to look at it this way...you're not missing Thanksgiving with her, you're taking care of yourself to try to make sure that you're there for her at Christmas. I'm sure that if your mom has lived 91 years then she is a wise person and would agree. Her child's health would be the most important thing to her, but since she can't be there personally to take care of you what she would want is for you to take care of yourself. I really hope this helps and I hope the holidays are easier for you. God bless :)