For heaven's sake do not let your parent's near that campus for interview day. Assuming that you get accepted, you will very soon be dealing with the very adult and serious responsibilities of medicine. If you can't handle traveling to a simple interview by yourself, just think about the leap you will be making in a few years when you are taking peoples lives into your hands. While there is nothing wrong with traveling with family per se, you may feel better about yourself for doing it alone. You need to focus. Take them for a visit at a later time.
I don't think the problem is if they travel with you for the interview. My parents drove up with me to Tufts, and my dad will be flying down with me to Florida in a couple weeks. And it's not because I'm not mature enough. I've studied abroad on my own, went to Israel without my parents, traveled throughout Europe on my own, so I can handle getting myself to an interview on my own.
I see no problem if your parents with you, as long as they don't actually enter the campus. My dad dropped me off the morning of my interview, so I didn't have to worry about train delays or anything like htat. Him and my mom took a walk around the city, did some shopping, and looked through one of those realtor books to see how much rent was

Then, end of the day, they picked me up.
For Florida, since Im under 25, I can't rent a car without essentially paying the same amount as an extra plane ticket, so my dad said he would fly down with me, and then we're staying on the beach for a few extra days, make a mini vacation. Fly down on a Wednesday, stay with my great aunt for a night, go to hte interview on Thursday, and then go to a hotel on the beach until Saturday. My job lets me make my own schedule, and my dad is self employed, and really, there is no point in flying back Thursday night after the interview anyway, because he would still be too tired for work on Friday, and if we stay Friday, might as well stay Saturday too because the plane ticket costs the same. There are some perks when it comes to going to interviews with your parents. I just wouldn't actually bring them on the campus.