Both destinations are served by Colombo (CMB). Since there's no flight route between them, the best way to travel is by road.
Aruppukottai
Fly to Colombo (CMB), then travel by road to Aruppukottai. Taxis, buses, and private cabs are available from the airport.
Thiruvananthapuram
Fly to Colombo (CMB), then travel by road to Thiruvananthapuram. Local transport options include taxis, auto-rickshaws, and state buses.