The Rams sway control is for catastrophic events, like the trailer getting out of control. It kicks in and applies the brakes individually as needed to bring it back under control and avoid an accident. It is not for ongoing sway control while driving down the road. If it's kicking in, you have serious issues and they need to be fixed rather than doing anything to the trucks sway control - which would be like shooting the messenger.
Have you adjusted the hitch so the front end of the truck isn't nose high? It really sounds like you have unloaded the front suspension.