if your rotor was able to make contact with the back side of the carrier (caliper) like that, then your spindle or bearings are shot.. the rotor is at its largest when new, so wear should have just increased clearance to that spot.

since the bearings are "ok" how did the new brakes line up?

a 1/4 inch of movement at the tire is a lot, so the inner tie rod is definitely not helping, tie rod can "lock" into place when the wheel is under load, (acceleration) however, it is more free to wobble, and shake the rest of the time. over small bumps, etc that you would normally not feel.

if the whole car is shaking, i would suggest also checking the rear axle bushings just to be safe.