16 and 17? do they not go out with friends without you now? Does the friend not deal with their pump at school without their parents?
Absolutely approach the other mom with this idea. It's a bubble but still public place on private land. Transportation is easy and plentiful, I can't see the other child being 16ish and not know how to handle their diabetic needs without help unless there is more to the story which is not our business. That's for their parents to decide or use as a reason to not let them join in the parks without parental supervision nearby.
And if the other mom say no, let your son go alone if he wants.. I was let go on property as a young teen but that was a different time, in a way it's safer now. Disney says you can get into the park alone at 14 (or is it 12?) and you can be 7 with someone 14 or older to ride (or is it 12). basically it's allowed in the disney rules for younger than 16 to be around the parks on their own or even with a younger friend/sibling.
it's a great place to give them some independence. it's a great way for them to enjoy some rides over and over when you want to do ones they don't as well. just structure when they must be with you or expected to be with you.. (you'll also find they tend to want to have family time also, just maybe not every single ride). It's a great way to say i trust you to do this and act like a young adult and I trust you'll contact me immediately if something goes wrong, no matter what the problem is.
Another way to look at it, in a year, they can just jump on a plane without you and do the whole thing which may not be disney as the destination.. let them be the very young adults they are. some states they are old enough to do that now as well as old enough to drive on public roads and get a car.
If your new to disney, For peace of mind, take some buses or monorails one day, let them see how you find your bus how security works.. Maybe limit them saying you have to txt when you leave and get there, you can only pick 1 park and no hopping. after the first day you'll loosen up even more. even if it's only your travel night you have time, head to springs and back, head to whatever park is opened go through security and then leave without entering the park and using a ticket (unless you want to that is). it'll be easier to say they can handle this when you know that they know what to do.