Fast answer
A car makes Valle d'Itria easier only when the route stays disciplined. Start with parking, then choose whether the day is about Alberobello and trulli, white towns, Ostuni, or the coast. Rail and transfers can help narrow plans, but they should not be assumed to cover countryside lodging or a full loop. Monopoli and nearby coast time usually need a separate day unless the inland plan is deliberately light.
If you only do one thing
For a first driving day, pick two main inland stops and solve parking before dinner. Add Alberobello as the major stop when trulli are the point, and keep the coast for another day unless the route is intentionally simple.