To qualify for either credit, you must pay post-secondary (i.e., after high school) tuition and fees. The credit may be claimed by the parent or the student, but not by both. If the student is claimed as a dependent, the student cannot file for the credit.
For each student, you can choose to claim only one of the credits in a single tax year. If you pay college expenses for two or more students in the same year, you can choose to take credits on a per-student, per-year basis. You can claim the AOTC for your sophomore daughter and the LLC for your senior son.