Why does it feel like my car shimmies when I accelerate and drive..?

couple of things it could be, wheels could need balancing, tyres might be wearing unevenly, tracking issue, brake discs could be warped or callipers partly seized if its under braking. check the inside of the rim for small weights for the balancing there should be some there, check the tread across the whole tire on each one, discs you can normally feel a lip round the edge of them if they are warped.

I recently worked on a similar issue on my son's Cadillac Deville where it turned out to be the front wheel bearings. On his car that meant replacing the hubs, as the bearings and ABS sensors were built as a single unit and those parts aren't individually replaceable, but I don't know about yours; you may or may not be able to replace just the bearings (if that's where the problem is).

To check, raise the car on jack stands. With two hands, grab the tire on either side and try to move it from side to side, then hold the top and bottom and see if there's any movement that way. Some side to side movement can be caused by worn steering joints so if there is any you'll need to try and figure out if it's coming from the steering or the wheel itself. Top to bottom movement, however, is going to point to the wheel bearings or ball joints since there's no reason for wheels to move that direction otherwise.

Let us know what you find on these suggestions and we'll do what we can to help out.

Fluid change your cvt transmission. It’s not life long transmission fluid. Change every 30k miles, 30k, 60k, 90k, 120k. My car would stutter when I accelerate and letting off the gas would stop it. Hope your problem isn’t a slipping transmission like mine was. Goodluck.