I had a long conversation with a, shall we say "rural" colleague of mine, discussing the virtues of having a Vet put an animal to sleep versus the "Old Yeller" approach. He managed to convince me that putting an animal down oneself was one of the most loving, yet extremely difficult, actions that a person could take. In general, the decision is, of course, between one of selfishness and generosity: is it selfish to let an animal live in pain, or is it generous to let them go? Is it selfish to put them down, or is it generous to allow them as much time as they provide themselves? It's never easy to say.
If, as others have said, your dog is merely urinating, then you need to tell your parents how selfish they are being. OTOH, if there are other problems (including, regrettably, the cost of pharmaceuticals for animals), then state them, as you've only said that she urinates.