If this is a problem I suggest never exchanging the children without a witness. If at all possible, have the exchange OBVIOUSLY (to avoid any criminal allegations) recorded by said witness. Be polite, pass on only information must be passed along regarding the children's health, upcoming activities or appointments, and leave any snipes, gripes, snide commentary, or anything not related to the kids' immediate welfare out of the discussion.
Exchanging children in a public area that is recorded is fine ... maybe ... but, not all cameras are monitored, some are not recorded, and just about all of them will lack any audio component.
I recall one exchange every other week in my area that got to the point of ridiculous. Parties from 75 miles south and 75 miles north would meet in a gas station parking lot for the exchange. The respective entourages grew to 2-3 cars each, handheld video cameras, and mom and dad making the exchange as if they were cautiously approaching a red hot iron. One or both would then make loud and public proclamations that they did not strike or say anything to the other, even as their respective entourages would hurl insults and accusations at each other. It would have been hilarious if not for the two small and terrified (and like psychologically scarred) children stuck in the middle of that circus of immature family members.
@eljess626, hopefully you and your co-parent can be better than the circus.