Why didn't the DPD take Kim's name at Kroger's, or search her car?
Because at the time Kim was telling a "good Samaritan" story that she found Crystal wandering by the side of the road. The DPD let her go with that. Only later did they come to understand her deeper involvement in the evening.
That isn't surprising to me. Kim wasn't suspected of anything and seemed, at the time, to be acting as a good samaritan. They had no cause to search her car.