I think an equally important topic in addition to your chance of getting in is your ability to pay. Do you know what your expected cost of attendance is at MIT (or your other schools), and do you know what your family can afford?
If military service is an interest to you, MIT does have ROTC programs. However, I would only recommend this if the military is truly the direction you are interested in, not just as a means to pay for school. Nuclear engineering is a preferred degree for the Navy.
FWIW- my S20 was also very interested in Nuclear engineering. NC State has a competitive application 3 week summer nuclear engineering program. It is very affordable, and gives a great overview of the field. (Application deadline is in April, so it isn’t too late).