If my wife graduate course work, while having a full-time job, does that include her as a college student?

Yes. As a Grad Student, you are eligible for the Lifetime Learning Credit. 

Calculating your credit

You can include the cost of tuition, fees and any books or supplies you are required to purchase directly from the school if it's a condition of enrollment. Therefore, if your professor recommends that you purchase a textbook even though you can still enroll in the class without one, then you cannot include the cost of the textbook in the credit. The maximum credit you can claim is 20 percent of up to $10,000 in eligible costs or $2,000. It can credit 20% of your tuition. It is limited by your tax liability.

As of 2019, the maximum benefit of the Lifetime Learning credit is $2,000. However, the lifetime learning credit is nonrefundable if it exceeds your tax bill for the year.