Cut Off Or Defend

'a' or 'b'?  

This is from one of my recent games. Answering Black's attack with the marked stone, White played the marked stone.

Obviously White wants to settle his group. Playing a Black gets quite a large corner and still can attack White.

But answering b cuts White into pieces. What kind of approach would you choose?

What I played  

Black 3 was wrong. It was not urgent. If White 3 then Black a. Thus there was a possibility to get an large move elsewhere.