If you travel with a group and there is an instructor in your group, every boat I have been on will allow you to train with that instructor, and most boat have instructors as DM's or dive leaders. As for cert level to do the dives on a liveaboard, my wife is open water certified, but has hundreds of dives and is an excellent diver. She has never been denied any dive experience. Competence counts.
DivemasterDennis
DivemasterDennis