My character is saying bye. We'll see the car pulling away, the final 'sure you don't want to come', etc. But then my character goes back inside. Is it INT. or Ext.

Ask yourself 'where is the camera?' The INT. or EXT. is so the crew know if they are setting up for an interior of exterior scene. Who's POV do we have?

It's almost never shot from both because that means setting up twice and shooting the scene twice, paying the crew twice, and bringing along two sets of gear.

All you get is more expense, more time, and horrendous continuity problems, especially if you can't shoot it on the same day and the weather changes.

Ian