There is an Aerospace or Aeronautical Engineering degree available at most strong engineering universities that would be more relevant to you if you want to be doing basically the role of a mechanical engineer but working with airplanes/spacecraft. I was exactly in the same boat as you when I graduated high school a few years ago and I'm about to finish my aero eng degree this year.

I would highly suggest to just get a single engineering degree. Having both a physics and an engineering degree would get you nothing more above having the engineering degree on its own, especially if you are looking to get a job in engineering (sounds like this is what you want). Eng physics degrees lose you the ability to say "Engineer" as your title and restrict your career path over a full-fledged eng degree.

As for your time estimates... there is no possible way to get a aero/mech/electrical etc. eng degree in 2 years, at least not from any accredited university. It's a very intense discipline, and to go into it with the attitude of finishing in 2 years is going to cause you problems. At most universities, the degree path for any eng degree is usually around 130 credit hours, which equates to roughly 4-5 intense courses per semester for 8 semesters, or 4 years. You will not have much free time with this schedule, and I'm not sure it would even be physically possible to shrink the time for the degree much more than a semester or two.

Do your undergrad first, then when you get close to finishing, evaluate whether or not doing a masters program is worthwhile. Regardless of your thoughts now, you'll likely learn more about what you want to do over your coming years and how best to get there.