One of the most common ways to remedy this is to do DB pressing but advancing on the terms of the weaker side. That's one way to fix if it it's simply muscular imbalances that cause it. If it's an injury, lack of mobility, pinched nerve or something else that causes it, then mobility drills with and without bands, foam rolling, ball rolling and even a visit to a physician could be required.
For now, you should avoid any kind of machine pressing that allows you to favor one side over the other like smith machines and non-unilateral machines in general. Using a barbell can be a good or a neutral thing given that you focus on using both sides simultaneously and end each set when the weaker side starts to fall behind enough for the bar to tilt.