This is a bit late, but I wanted to respond in case the problem is still occurring. My partner is a retired police officer. Now maybe it is just their policy or the laws of my state, but police stations are public buildings, paid for with our tax dollars. While the poor desk officer may not like to see people sitting around waiting for a custody exchange, ask for a supervisor to come to the desk. Ask them for the specific code section of the penal code or municipal code stating where custody exchange are not allowed.
If there is a law, then you can ask a judge to order it, which will then allow it, even if the police don't like it. But, in fairness to the officers, make sure your child acts properly, have toys, games, something to keep him busy so he isn't running around being a pain to everyone there.
If you child is showing a lot of negative behaviors, time to get him to a therapist where this can be documented by a 3rd party to show the court why visitations need to be stopped or supervised.
Hope this is some help.