Who’s going to pick you up at the airport?

Did she think this through somehow?

you could "miss the fight"

I doubt she thought enough to buy a refundable ticket and won't likely do it twice

what did you do to piss her off? it's only for a few days be nice be polite and you'll survive.

You remember that line from Harry Potter 3, “I will if she does”? If Aunt Marge won’t be nice to Harry, why should he still his tongue? If these relatives don’t like OP and vice-versa… this won’t end well.

If they don’t like you and you don’t like them, think of all the trouble you can cause!

Then, to save yourself and your relatives some hassle, just don't go - tell your mom you missed the flight and hope she doesn't do it again.
Alternatively talk to your mother and tell her what you think about both these relatives and the way she is behaving by doing something like this to you.
Good luck!

See if you can exchange it for a different location, swipe a credit card on your way out, and have a vacation.

Give the TSA agent at the airport a really big smile and tell them you're sooo happy to finally be off the no-fly list.

Have you told parents this, and why you don't like them and they don't like you?