First off everything I know applies to the OLD GI bill...I'm assuming that is the one you have. I used it for training, and while I was a CFI, I was the school's VA administrator (trained by the VA).
I have heard (but not verified) that the new GI Bill will pay for higher education only, not VoTech...so no truck driving school, welding, or flight training.
Normally, you can only be enrolled in one training program at a time under VA. I already had a BS, so I used it for some post-grad and certificate programs, and finally for some of my flight training. Every time I switched programs I had to do a brief paperwork drill.
For flight training, the VA will not pay for "recreational" flying. This means you must pay for your PPL out of pocket.
Since the IR could also be purely recreational, you must enroll in a concurrent IR/Commercial program...this will alllow you to get paid for the IR. Any VA school will offer this under 141. Once you have the commercial, all subsequent professional ratings (CFI, MEI, type ratings) can be covered by VA.
A VA-approved 141 school will have a trained administrator to handle the VA paperwork. Keep copies of everything (forever) and double-check it all yourself. It will take weeks to get your first check, after that they should roll in regularly. Note that you will have to pay your training costs up front, and will get re-imbusred by VA after the fact. But don't deposit a large amount of cash with any flight school...pay as you go on a week-to-week basis. Otherwise you risk losing it all in a BK (far too common), or if you drop out or change schools they may not give you quick refund.
The VA will now pay for some expenses which they did not in the past...books(?) and checkrides.
As far as concurrent enrollment in UVSC's flight and degree programs, you will need to talk to the UVSC VA administrator about...maybe it's possible if they have the flight program setup as part of the degree program.
If you need to do a full four-year degree program, and have to choose between using VA for flight or college, you are probably better off using VA for college. The flight training reimbursement will be a MAXIMUM of 60% of what you pay for flight training, grand-total not to exceed what you would have been eligible for during a 36-month college degree program. Odds are high that you can get more money out of VA for college. Also the college payouts are just a monthly lump-sum, which you can use for food, rent, beer, etc...the flight training payments will be based soley on training already accomplished and paid for by you.
Also in many cases VA-approved 141 schools charge higher hourly rates...they know you can afford it. It may well be cheaper to use VA for college and train part 61.