We actually asked about this at McGill. One daughter was a very talented musician, and also wrote her own music. She had considered being a music major but changed her mind after a music related tour of Europe. She also found that you get tired of your own best songs, and people keep clamoring to hear them. She since then has been neglecting her music to focus on academics, and if all goes well with be a DVM in about 9 1/2 months from now. She was however very interested at the time in continuing her music and she still does intend to get back to it once she is out of university.
Engineering is a very intensive major (which might be one thing that it has in common with veterinary medicine). You are likely to need to focus quite solidly on engineering while you are a student. Once you graduate however, you will have more time and extra energy. Having worked in high tech for my entire career, I have known quite a few engineers and mathematicians who also play music, and in many cases play music very well. I have multiple times attended a music event and seen people I knew from work get up on stage and play (and I have myself gotten up on stage and played on multiple occasions).
It certainly is possible to continue music lessons while you are at university in Canada. For example we were told at McGill that the various performance music professors augment their income by giving lessons to McGill students who are not music majors. This does imply that you would pay for the lessons. However, the difference in cost between US universities versus Canadian universities is enormous. You could pay for music lessons for probably several lifetimes given the difference in cost. McGill and Toronto are both of course superb for music, and UBC is quite good. I have also heard good things about McMaster and Queenâs (one family friend is a professor of music at one of these universities). I would expect that any of these schools would have professors who give music lessons on the side to non-music students.
But a bigger concern that I have is the difficulty in finding employment after graduating from a university in the US as a Canadian citizen. In my experience first with a degree from MIT, and then with degrees from both MIT and Stanford, this was very, very difficult. Canadian employers prefer to hire graduates from universities in Canada. American employers prefer to hire graduates who have the legal right to work in the US. For me this was a VERY BIG DEAL and a major problem. I do not have any reason to think that things have gotten better over the past several decades.
Do you parents fully understand how much university in the US costs?
I agree with other responses that you should only ED to a university that is clearly your number 1 top choice.
Predicting whether or not you will get accepted to one of the top universities in the US is exceptionally difficult. Admissions in Canada is relatively predictable, and is largely based on merit. Also, top schools in Canada do have enough spots to accept all of the academically superb students (such as you) who apply. Admissions in the US is only partly based on merit, and the top schools get many, many times more fully qualified applicants than they have places to put them.
I also agree with other comments above that Rochester is an interesting option. It has a great music program, and admissions is way more likely compared to somewhere like Stanford or Cornell. However, I still wonder what this will do in terms of your chances to get a good job somewhere around about 5 years from now. I really think that you would be way better off at one of the top universities in Canada, and taking music lessons on the side.