My parents went to the airport to see my uncle off.

Literal

Parents [topic-は] uncle [object-を] see-off [purpose-に] airport [to-に] went.

見送りに行く uses the masu-stem + に pattern for purpose of movement: 'went to see off.' Two に particles serve different roles — 見送りに (purpose: 'in order to see off') and 空港に (destination: 'to the airport').