The way I understand it, you have tapped into the positive for each light with an output from the 4200 mini, but the lights are wired together at the relay. When the mini powers one side, power backfeeds through the wiring and goes to the other side as well, making them both light up. The flasher alternates, powers the other side, and it backfeeds to the first light, making them both light up. That's why it isn't working properly.
To fix it will require four diodes, which are components that allow electricity to only flow one way. (think a check valve in plumbing) You will need one between the relay and where you have tapped the 4200 outputs in on each side, allowing the 4200 to control each side without backfeeding the other. You will also need one on each output, so that when you have the lights on steady, they are not feeding back into the 4200. This will allow you functionality of your flasher but you can still safely override to steady with your existing switch. Feniex is correct, the 4200 mini will not allow you to override by itself, but it can be done...