My LLMD isn't affiliated with a hospital either. But if your primary care physician is, then there's nothing to worry about. I'm trying to keep my PCP updated with my Lyme treatment. This way I have two MD's who know what's going on with me. Also, it helps to educate my PCP about Lyme and hopefully she'll recognize the next case that comes her way.
I would also ask your parents why they think it's important for your LLMD to be connected with a hospital. You need to know what hospital your insurance covers. If you don't have insurance, then if needed, your LLMD would tell you where to go.