Q. Is my child considered a full time student if she is doing an online graduate program at a university that offers in person classes?
A. Simple answer: yes. As you surmised, the key is that the university offers in person classes, so it is probably an "eligible institution".
Whether she is "full time" is determined by the school's definition of full time. But, she is eligible for the Lifetime Learning Credit regardless of her class load. Grad students are not eligible for the more generous American Opportunity Credit, which requires half time or more.
