Like others have said, you can't make your family and gf change their ways but you can try to find out the underlying reason why they don't want to change and go from there.
Your gf not wanting you to go to the gym b/c it'll hurt your relationship sounds familiar to me. I used to work out often, wanted to go into the military and then onto a federal law enforcement career, but my husband made me stop working out. Why? Because I think he was jealous since he couldn't do those jobs (he's disabled), and worried that a fit body would attract other men. I am not saying your gf is jealous, but you should be asking yourself why she's afraid you're workouts will hurt your relationship. She's probably afraid that working out will be hard for her, that if you two try together that she won't be able to keep up with you, and that soon you'll become thin and not want to date her anymore. You should try to calm her fears about this, and maybe try doing something together at least a few days a week, like maybe take a walk after dinner, etc. to make her feel included. Start out with something really easy and as she gets more fit you can try something a bit harder.
Your family may think that you eating healthy is your way of trying to be better than them, or saying that they were bad parents for not having more time to make healthy meals, etc. I don't know how your family does grocery shopping, but I'd consider trying to look up your own healthy recipes, and whenever grocery list time comes around to put down those ingredients and explain to whoever does the shopping (or offer to make the trip yourself) that those items are intended for a meal that you're going to make for everyone. And actually make a dinner for everyone that week. If you slowly incorporate healthy foods without saying "see this is really healthy" might get them to start having more of an appreciation for better quality foods, and if you do the cooking for that meal it's not like you're trying to put if off on mom or whomever.
I also second the min-fridge suggestion, I have my own and it's great, no one can eat my greek yogurt now!

And, they're not too expensive either.