The University of Delaware is a very good university. I can see the point that your parents do not want to pay quite a bit more for a school that is equally good compared to U.Del. This makes sense.
I have seen a few cases where students attended an out of state public school that was just as good as their in-state public school, and only twice the price. This is okay if the parents can afford it, but is an unnecessary expense.
This makes sense. It sounds like they know you well.
The experience that you get while you are in university can be very important. As one example, I have heard that it is difficult for someone with just a bachelorâs degree in biology to get a good job. My younger daughter graduated with just a bachelorâs degree in biology, and had the exact opposite experience. Once she started looking for a job she had 3 good offers in five weeks. The issue was that as a sophomore in university she discovered that she really liked lab work and was good at it. Then she spent three years getting as much lab experience as she possibly could. That lab experience was what appeared to help her get good job opportunities (all of which sounded to me like she would be doing something similar to what she had been doing for three years as an undergraduate student).
Similarly, my wife, my older daughter, and I all think that our work / lab / research experience was a big part of what got us accepted to very good graduate programs. What we each did was quite different, but was right for us and right for the graduate programs that we applied to. My younger daughter is only applying to graduate programs right now so we have yet to see how this goes.
The fact that you already have lab / research experience at U.Del is a very good start, and to me seems way better than average for someone who is still a high school junior.
When I was in grad school the other students in the same program had come from a very wide range of undergraduate schools. A few doctors have told me the same thing, as have people who went to other types of highly ranked graduate programs. I think that you can get a good start at U.Del. which will be a good first step towards either medical school or some other form of graduate school.
And also applying to a few reaches makes sense to me.
I think that you are doing well and thinking about the right issues at this point.