Backcourt violation?
 

Team A has spot throw-in just past division line in front court on sideline.Team B pressures all players on in bound pass. Team A player receives throw-in with one foot in frontcourt , one in backcourt.The ball remained in the frontcourt and first dribble was in frontcourt.I make no call and play continues. Did I blow it?

If the player has one foot in backcourt he has backcourt status, as does the ball when he catches it. If he starts his dribble from this position, no matter where the ball actually bounces, it continues to have backcourt status until the ball and both feet all touch in the frontcourt.

no violation in the OP

Nope. You did it right. The rules are different for a throw in. 9-9-3.

You did it right. But why do say the ball was in the frontcourt when A2 initially caught the pass?

Ball location
 

Basically the ball was still across the division line in their frontcourt with the other foot vs the other foot in the backcourt as i saw it.

But does the position of the ball "in the air" matter? See 4-ball location.

Clarification.
 

When the ball was inbounded to A2 she caught the ball with one foot in the backcourt and one in the frontcourt with the ball in her hands still on the frontcourt side of the division line. Her first dribble was in the frontcourt and the game continued.I hope this helps.

What we are trying to say is that where the ball was during its flight is not relevant. Your ruling was correct but it has nothing to do with where the ball was. Has to do with where ball's flight originated from (throw-in by A1) and where A2's feet were when she caught the ball.

Also remember that on a throw-in, if A2 catches the ball while airborn (and is the 1st to touch the ball), it does not matter if the first foot to touch is in the frontcourt or backcourt.