A competent alignment shop would check everything for looseness for two reasons.
- Their work wouldn't hold and you'd complain about looseness or tires wearing unevenly
- They can make more $$ if they find bad things in the inspection.
If you no longer trust the dealer, find a competent independent alignment shop and have them look for loose stuff. There are over a dozen things it could be, from loose wheel nuts to wear in the tie rod ends (inner or outer) to worn control arm bushings to bad ball joints to a loose steering rack.