First of all, look up an old thread about justifying our profession to civilians like your folks - there is some good info that might be of use. I am not particularly lucid this evening. But -
Lots of young people face the same issues - how are you going to get there, how are you going to get around once there, where do you live, how will you pay for food etc. This is the time to learn, this is how you learn. Presuming you are working on becoming an adult, you can remind your folks that it is vital you start figuring out how to do these things so you can survive as an adult in the world. Our profession is all about handling details and making things work, so solving all these still-unknown issues is a great way to find out that this is the right profession for you as well as what you are capable of accomplishing on your own.
And, college is the time to experiment, to try things out, to discover what you do or don't want to do. Isn't it better (tell your parents) to do this internship now and know now; you can always get a normal job but these opportunities go away once you are no longer a college kid. This is a great experience that will either lead you onward into your career, or be a wonderful memory of your wild college days when you are settled in something far more normal, right?
Take a deep breath. It's hard for parents to see their kids as young adults, to let go of them and let them walk into their own lives. Your parents are always going to be concerned about you, your ability to make it on your own, your happiness, right? And ours is a challenging, itinerant profession without any guarantees, so their worry is justified. But if it makes you happy, they will see that. And if you can introduce them to working SMs who are making a living, that might calm their nerves as well.
And - I should add - my dad never ever "got" tech week and why I wasn't available at certain times to drop everything and call or visit, in spite of my earning my living as a stage manager for some 40 years now.