There's no magic $1000 credit for college. The rules are very restrictive, and in this specific case, married filing separately is an automatic disqualification for any credit. Also, she can't get the credit if she doesn't pay qualified education expenses (because the VA covers it).
If she is paying qualified education expenses, I see no reason she would not be eligible for either the AOTC or the Lifetime Learning credit on a joint return, unless you know of some other factors. For the AOTC, qualified expenses include tuition, any fees that are required for her course of study, and any books or materials required for her course of study, even if not paid to the school. For the lifetime learning credit, allowable expenses are tuition, fees books and materials but only if required to be bought from or paid to the school directly.
