I don't think Nymphadora's parents knew she was part of the Order;

That's an interesting thought. I always assumed that Ted and Andromeda were informed about what's going on. My issue with their absence from OotP is not so much directed against them (as in, what were their motives) but against Rowling, who could have mentioned, even in passing, what they were up to. I hope she will tell us about it in future books.