Tire pressure can and certainly will play a roll in how your vehicle handles, but it sounds like you might need more than that. In general, I tend to run under the maximum inflation spec for the tires, as I rarely run at the rated load capacity of my tires. When I ran 33" mud-terrains, I was at about 32 PSI in the front and 28 PSI in the rear, as that seemed to be the happy place on the street. With my new 37's, I expect to be a bit lower than that.
I would check your track bar bushings and tie-rod ends for excessive wear/movement. A good way to do this is to have somebody turn the wheel back and forth while you sit in front of the rig and watch everything...take a video if you can so you can zoom and focus in on something later if needed. Next, I'd check the toe-in and caster measurements, as your static alignment specs will in large part determine how the rig drives down the road and feels.
Tobin