I had a reenacting organization meeting there a few years ago. One of the guys there is/was the curator at the Patton Museum and used his connections to get us in the storage areas. They have some really cool stuff.
First, talk to the financial aid office. If your mom is denied the PLUS loan, you will qualify for additional Stafford money. And the university will be able to determine if she will be declined or not.
A private school loan is where you go to a bank, speak to their lending agent and get a loan through them. They will have a special product to sell you with a lower interest rate than their general loans. It's possible to shop around and get several different loan terms and play them off each other for better terms.
What I would recommend--If You Can--is that you determine how much you'll have to cover, determine how much money you would make with a part time job during the school year and set up a payment plan with the university.
It's best not to have all kinds of loans from different lenders as it can get confusing having to make a dozen different payments each month.
SportsCenter a segment some time ago--several years--where they put all kinds of sensors in John Lynch's helmet (Lynch was the hardest hitter of his time) and they equated a full-force hit to being hit by a city bus.