It's not poverty. It's not coded for poverty. It's her living out in the middle of nowhere because she's paranoid.One of the issues of trying to make her feel coded as a poor person but in a universe were poverty isn't even a thing anymore on Earth. While you can see what they are going for it doesn't really make sense logically in the Star Trek setting.
She's just a nonconformist. She's the Dr. Servin without the spirituality.
Assuming trailer=poverty is ridiculous.