Poor Milo is in bad shape and I am so glad you’re seeing the vet right away after all. As Beka said, discussing all of the options for her with the vet, every possible scenario, is really the best way to make an informed decision on her behalf. If it’s just that she’s about 3 or 4 years old, and will have a healthy life once she has surgery which includes the spaying so this won’t happen again, then you can plan on many more years with her. But after age 6, she may not handle the surgery well depending on her overall health, so you can ask the vet her educated estimate of the percentage of recovery and quality of life post-surgery, if she comes through it. Think of putting her down as the way to end any suffering she may have from now on – if that’s the case, your parents may be right. If it’s just a way to save the expense of making her well, that’s not a good reason and vets can work with you on payment plans to pay off a bill gradually, like with a credit card, in order to do the best for her.
Let us know how it goes. {{{{{{{{{{Hugs to Milo and You.}}}}}}}}}}}