My first mistake...
 

...was mentioning to my partner at halftime that our game last night was flying along. Sure enough...double OT.

I'm thinking we screwed up a minor thing at the end of regulation. I'm L, and we're tied in the final seconds. B1 shoots and misses. I have a foul on B3 on rebounding action as time expires. Team A is in the bonus, so we're shooting one and one with the lane cleared. She makes it, it's over, misses and we're going to overtime.

She missed and on we went.

On the FT's, both teams went to their benches. Should the players that were in the game stay on the court, since the 4th quarter isn't over until the free throw is made or missed?

That's not really the intent of the rule. It's to prevent a team from going to the locker room at half-time.