Where would be a good place to do the mandatory ritual of shopping in LA, within a short drive from LAX, as we'll hardly have a couple of hours left for this ?

Well, Manhattan Village Mall is about 15-20 minute drive south of LAX on Sepulveda Blvd. Fairly small as malls go, has two Macy's (women's on the north end, men's on the south end) as well as a number of nice speciality shops, nice restaurants outside the mall, both chain and non-chain.

Also close to LAX is Westfield at Fox Hills in Culver City which is a bigger mall than MB Village.

http://www.westfield.com/culvercity/

Or you could go to downtown Manhattan Beach and shop the many boutique stores, have a nice lunch, walk along The Strand.

If you go to the Manhattan Village Mall, good lunch options are L.A. Food Show and Tin Roof Bistro (ask someone to point it out to you).

MB Village mall:

http://www.shopmanhattanvillage.com/

Closest is the mall at Culver City. Also some limted stuff just north on Sepulvda in Westminster, but there isn't much there, just basics, fast food, drug store, supermarket, etc.

Not Westminster. It's Westchester. IMO not worth a stop unless you want to go to In 'n' Out.

Check out the directory for Plaza El Segundo, (plazaelsegundo.com), on the east side of Sepulveda right before you get to Manhattan Village Mall. If you have teens with you I think the might like it better. It would also allow you to be outside for your last hours in LA. If it is boutiques you are after then as Jean suggested go to downtown Manhattan Beach. Happy shopping!

BTW, LA Food Show in Manhattan Village Mall is aparently closed.

Wow. I missed L.A. Food Show's closing. And darn! We're going to miss it a lot. I do think it was a bit of a hobby for its owners who are the guys who started California Pizza Kitchen.