I would recommend starting with checking the car(s) for the error messages generated when the charging rate slows down. I am not an expert on the electrical side of setup for wall connectors / outlets, but this normally happens because the car is "detecting something" and slowing the charge rate down in response.
The "charger" is actually in the car. People call them "wall chargers" out of convenience, but they are simply fancy extension cords with some technology in them to announce to the car how much power is available. It is the car which decides what speed to charge at. If the car starts at a higher speed, then slows down, its normally because it detects a problem.
There are a few different problems that can occur, but if "it works perfectly with this one hard wired wall connector, but does not work properly with this wall connector that has a pigtail on it", the issue is likely the connection in either the wall connector to its pigtail, or the outlet you are plugging into