For engineering, you can have the opportunities you seem to want staying at Vandy. Many students do internships that are an “aside” to their actual eventual jobs.
I would suggest that you head over to the career center and have a conversation with them.
For most engineering jobs, you will get a huge amount of training on the job. You will learn the culture of the company as well as their way of doing things. Many engineering firms have mentoring as part of the probationary period.
I think you can achieve your goals from Vandy or Pitt. If you really want to move back to Pittsburgh, then apply to transfer.
It’s my opinion (and I asked my career engineer husband the question) that your engineering concerns are not well founded.
I will add…my DH thought he wanted to only work on the technical end of engineering…but he had an extremely rewarding career as a consulting engineer.
So…keep an open mind!