This play a very important role indeed. Don't forgot her son's tuition that is mentioned even more that her car (and in fact serves as an excuse to meet the son's dumb "friends"). As Justaphase said, this is also an important factor to keep seeing the boss. The car was a birthday gift from Hutch and she wasn't as keen to have one. In fact she says to Hutch that all that matter to her is being together. Her crying in the car is because is defective in the worst moment and for all the stressful situation, not for the attachment to it.She does it to keep her own social and financial status.
I think her going to see the boss in the first place is because she feels that her husband is hesitant, and she has to act firmly to save her status (which includes her family itself). Then it becomes some sort of challenge between her and the boss. That's why she insists to go to the dinner, until she realizes once at his home, that he was testing Hutch and not her. Thus, this will also explain why she accepts to sacrifice, because she feels that she was the "original sinner" so to speak.