You will run into a couple issues most likely: 1) not trading in your current open auto loan and 2) debt to income. I highly doubt MB Financial will play ball with you, and if they did, it almost certainly would not be a promotion APR (like 1.9% etc). If you insist on doing this, I'd think you'd be better off getting approved with a credit union so you know exactly where you stand. The dealership will most likely find a bank to do the deal (because you're putting down so much), but they will probably shotgun the app to 20 different lenders (meaning all those inquiries will show for 2 years) and I don't think the interest rate would be favorable.
Obviously you didn't ask this, but just my two cents - when you buy this expensive car for your parents, remember you're carrying that debt with you for years. So, while you may live with them now, you might not want to live with them in 2 years. Then you'll have to deal with qualifying for your own place with a $700+ car payment in your name. Believe me, I understand wanting to do something nice for parents, but if my parents needed a car, I'd be getting them something more practical.
Hard to say what the rate would be. I work in finance for a franchised car dealership, and I would be shocked if you were able to get a 6% rate. It's not that your credit is bad, you just have a very thin file and limited income. Even though your living expenses may be at a minimum for a while, most banks won't allow for car payments to eat up 40% of your income. When you get closer to buying time, I'd definitely try a credit union before going to a dealership. If you're not a member of one, you may want to look into joining one (I like Navy Federal a lot, if you have a way to get in with them).
Take over your own payments and let your parents do what they want with the money they were spending on you.
A parent would much rather see an independent kid. Is giving a financed car really a gift or another obligation to you parents?