If you finish your AA at your community college with the kind of GPA you earned in the first year, you are almost certain to have more transfer options than DePaul. Here is one recent thread on that topic: http://talk.collegeconfidential.com/transfer-students/1783917-community-college-to-the-ivy-league-two-year-testimonial-p1.html
I find it difficult to believe that all of the other public universities in Illinois are as bad as you describe. Please don’t take the list in the USNWR so much to heart. The difference between 149 and 121 is not as big as you seem to be thinking. What matters for your major, is whether or not graduates of the college/university that you attend do get jobs. The Career Centers at each campus can tell you where their graduates go and what their starting salaries are.
Generally speaking, public universities have lower 6-year graduation rates than private colleges and universities do. Reasons for that include the fact that many public universities are essentially obligated to admit any high school graduate from the state, so a lot of freshmen who aren’t ready for college flunk out before Thanksgiving. Another typical reason is that students who don’t have the money for a private college or university end up at the public university and must work while they study so they may take semesters or years off just to make money before going back to school, or they can only afford to study part time. Students who are committed to their program and who don’t have to take time off to earn that much money do indeed finish on time and go on to be successful in their lives.
If your parents want to put themselves into debt to the tune of $120k for the next three years of your college education, I can’t stop them. But please run a loan repayment calculator with your parents, and talk about the sacrifices your family will be making in order to pay off this debt. Will your parents be paying down this debt instead of saving money for their retirement? Do they plan to take on second jobs to cover this? Find out what kind of loans these are. Federal PLUS loans can be forgiven if the student or parent should die. However, that benefit is not built into all private loans. You and your parents may want to consider taking out term life insurance policies on each other to cover the loans in case of that kind of disaster. Right now you are planning a major that usually leads to well-paying jobs. But not all students find those jobs. It can take a very long time to dig your family out of this kind of debt.