The kid should be allowed to get a job if that is what they want to do. I think it is good for teenagers to start working at 16, as long as it doesn't get in the way of their studies.

As for how it works with "partial custody" (not sure what that means), it could be possible for the teen to give the boss their schedule of when they will be with you, so that they are not scheduled to work on those days. Most employers are used to working with the crazy schedules of teenagers if they employ them. BS19 works for Lowes, and they were very accommodating to his football schedule.