Dumbell work is the way to go, to an extent. Continue with them but also start normal flat bench. This will help you with figuring out a form that keeps the lift out of your shoulders and throws it into your chest. You may want to start with a closer grip on the barbell, usually about a thumb off the smooth part. Most guys want to put a finger on the outer line, this put some of the weight into the shoulder. Keep your grip close, and when you press, keep your elbows in tight and the bar towards your nipples. Your going to have to play with this a little, to each their own finess, but this will start to eliminate the soulder from the press. Basically this is touching in on power lifter form. Toy around with it to get everything dialed in but this will hit chest much more than shoulder.
Continue to use the dumbells, that is key. Once you get the feel for the new grip on the barbell, use that same style on dumbells. I would'nt worry about doing isolated presses for your right side only. This may be leading towards an overtraining situation. Your right side will start to build up, it does'nt have a choice. Worst case scenario, talk to a trainer for a session and tell them your problem. They will be able to show you the different forms that will keep the press in your chest. Explaining it over the internet is a little hard to do.