My father was diagnosed with reactive hypoglycemia before I was, and he actually miseducated me. It was only when I came online that I discovered how WRONG everything he told me was that I began to gain an understanding of what was going on.
Since then, he still tries to "educate" me, which annoys me more than anything. It's almost like he wants the wrong information to be right. So I understand how frustrating educating your parents can be, because I can't get through to my father.
The first thing you need to do is make an information sheet to go in the kit. It should have a list of if/then statements. Say, "If blood sugar is below 70 and Stephanie is responsive, then give one juice box", or "If blood sugar is below 40 and Stephanie is unresponsive, then give glucagon".
I assume this box is really for emergencies, so it's unlikely you'll need insulin in there. You'll need a meter in there, glucagon, glucose tablets, maybe cake gel (it doesn't crystallize like honey does, but it works well, too). You should probably include some alcohol wipes in there, for cleaning off your fingers to test your blood sugar.
You'll also need a detailed list of instructions for testing blood sugar. Make sure your parents can follow it easily, so test it out on them. Maybe you can tape a cheat-sheet to the inside of your meter case of blood sugars and what to do for each range.
You'll also need a detailed list of instructions for giving glucagon. The same applies here as for testing blood sugar--and walking them through how to use glucagon a few times may also help.
Finally, you'll need a sheet of paper with important information on it--your insulin dosages, which insulins you use, your endocrinologist's phone number, any other medications you take, etc. This would be useful for them to bring to the hospital if you ever go for any reason, even if it isn't diabetes related. Including the fact that you're on MDI is very important here.
I wish you luck with this. At least, it seems like your parents are interested in being involved enough to protect you.