The problem is, my husband and I still want to spend time with my family but these occasions always focus around my mother's cooking. My parents don't believe in going out to eat, and we're not sure if we can politely bring a dish or two and have my husband eat only that. It seems rude.
Any good advice on how I can approach my mom about this again, or ways around this?
I think you have a few options: the most uncomfortable is to be honest with your mom, tell her about the hair incident, let her know you've had similar experiences in the past and ask her to improve her kitchen hygiene. This won't be a fun conversation, could make your mom defensive or upset and might cause a rift between you two. Even if she were to make changes, being grossed out by someone's cooking is hard to get over much like one incident of food poisoning can put you off a particular food or restaurant forever.
Less direct, less brave but possibly more effective options are to actively organize get-togethers with your parents that don't revolve around a home cooked meal, insist on taking them out to eat (you don't say why they are averse to eating out - let them pick the place and insist it's your treat) or, as you say, bring some dishes to contribute yourself ("I just learned how to make x and am excited to share it with you.").
Good luck with this delicate situation. Readers, what advice would you give?