When a custody agreement says “parenting time every other week” what exactly does this mean?

I hope that your custody agreement says something more than just "parenting time every other week". A good custody agreement will spell out the dates and times that he's supposed to pick them up and where, and will say who's supposed to pick up, who's supposed to do the drop off and things like that. If yours just says "parenting time every other week" and nothing else then he is probably not breaching the agreement since it is too vague. You need to talk with an attorney as soon as possible to work on getting more definite language in your custody agreement so that questions like this won't come up again in the future.