I would make one more, very direct, request to the rescue as advised above. No hints. No starting your request with mushy words like “I hope…” or “I’m wondering if maybe you could possibly…”.
Just: “I need to ask if you will take xxx mare by xxx date. We have no money and will run out of hay by this date.” Have this conversation with them tomorrow, don’t put it off. It won’t be as hard as you think.
If they don’t agree, or give you another mushy answer (“we’ll see what we can do”) then you have to consider that a firm “No”. You’ve already asked a few times, and there’s a good saying to keep in mind (in lots of life situations): If they wanted to, they would have.
So then I would focus on assembling the funds to ensure euthanasia rather then ending up on a slaughter truck. Odds of finding a “good family” buyer out there for an old horse with limited use are about the same as winning lottery. Especially at this time of year, when everyone’s winter hay has already been purchased. A slaughter-bound truck would be a terrible and drawn-out ending for this mare. Your way to prevent this is euthanasia. I’m sorry to be so blunt, but it’s reality.
How to make euthanasia affordable: i you are in a rural area where guns are permissible, and if you have a skilled gun owner in your family/friend network, putting a horse down with a gun is one of the most humane ways to do it.
Disposal costs can be reduced if you schedule in advance with a rendering company to find out when they’re in your area.
Ask your parents to pay for this and you’ll pay them back monthly. Print this thread out and show them if they don’t believe that selling her is not going to be realistic.
Give up your cellphone for the next year and get a pay-as-you-go type phone for emergencies. And yes, get a job-- I know your 4.0 GPA is very important to you, but a job and good grades are not incompatible. (Having a job also makes it easier to say no to family caretaker requests that should not always fall on your shoulders). A 4.0 student would probably make a great part time employee for a vet-- see if the vet would let you work off the cost of euth.
Good luck, and thank you for caring for this horse. This coming year will require a lot of sacrifice and hard work on your part to ensure that she doesn’t suffer, but you seem like the kind of smart, strong young woman who can tackle this problem successfully.