. The smaller wheel offset will change the front wheels Toe Out On Turns angle. The inner wheel circle will be slightly smaller and the outboard wheel circle will be slightly larger but won't affect straight line travel. 55mm to 35mm = 2x 20mm = 40mm centerline difference between the wheels. Slow turn scrub may increase or decrease depending on manufacturer original specifications. For instance: keeping the same steering components on vehicles with different chassis lengths. Rear wheels offsets do not affect the turn radius scrub.As John stated above...you have issues. First being your tires and rims. From the pic, your stance is wider then the factory wheels. From the looks of your pic I would guess you have a+35 offset...factory is +50, thus moving the mounting surface (or dead center) of your wheel further inward. I'm guessing your tires are wider then the factory 245/45/18 tires. Guessing you have 19" or 20" wheels. This is going to over-pronounce any little issue that might have been minor with the factory wheels and tire size. And the feeling of that issue is going to go up exponentially for evey 1" of diameter larger then the OE 18" wheel. This was a HUGE issue for Lincoln when the Navigator went from 18" wheels to 22". To give an example of what I mean by over-pronounce.... I just put 19" wheels with 255/40s on my car. I've never had a problem holding the steering wheel straight at 75mph and the car staying there. Never had any play in the steering wheel. With my new wheels, the car now "dances" back and fourth in the lane. I also have a bit of a "dead spot" (basically a wear spot when moving the steering a touch left/right and the car does nothing) that I now feel in my steering...it's about 1/4" of an inch of steering wheel movement, something I've never had.
Now the next item. How many miles on the car? Chances are it needs shocks. You have to remember, this is a ~12 year old car. Shocks wear...and for most, it's time to replace them. I see this being a common topic next spring/summer on the forums.
I know the feeling you're talking about. It feels like the car just wants to get away from you if you make any sudden movements or hit the brakes at the wrong time. Generally in the dealership, this used to be caused by bad shocks/springs and incorrect alignment. And in extreme cases the power steering rack needed to be replaced. Generally though on cars now days, the rack and pump get replaced together. Good luck, hope you figure out the issues and get it "in tune" so that you can enjoy your car!