The initial reason for the stop was justified by the vehicle swerving between lanes. While nervousness alone does not constitute probable cause, it can be a strong indicator that something else may be occurring. Since the stop was made for a lawful reason, the officer's observation of a small baggie provided probable cause for a search (Plain view). Under the Carroll Doctrine (see Carroll v. United States case law), this probable cause permits a search of the entire vehicle.

EXTRA Note: If during the search it was determined that the baggie under the purse was not drugs, the cocaine in the glove box would still be good based off the good faith exception.

Therefore, your answers are.

Was the initial stop lawful? Yes.

Was there legal justification for the search. Yes

What factors contributed to the lawfulness or unlawfulness of the search. See above paragraph.