White mucus most likely indicates an infection. I’m not familiar with snuffles but it could be some sort of upper respiratory infection (URI) since they have very sensitive tracts or like you said, something could be stuck up there that is irritating her nose. Illnesses can develop quickly in bunnies so within these two weeks something could’ve easily happened. Either way it sounds like she needs to be checked out by a vet. Unfortunately an ill rabbit can cost quite a lot of money and care so it’s important that your parents understand this as well.
Is your vet rabbit savvy?
What’s her overall diet like and have you tried other kinds of hay rather than just switching the brand? If you’re currently giving timothy hay and she doesn’t like it, you could try other kinds of grass hay like orchard grass, oat hay or meadow hay. Orchard grass in particular is a favourite for many buns as it’s sweeter and softer than timothy so you could start with that. Oxbow is a common brand but you could try other brands as well 