No, why would you want your home to be finished twice?

How can A sue B is A's problem, you don't have to worry. Why are you getting double payment or have your house done twice? Or are you keeping the extra money as "winning"?  

A and B is only required to fix their own damage.  Just because A overypaid for his damage, doesn't mean B should also overpay its damage.  

Because A overpaid, and B only pays for its own damage, you might have some extra money left over.  I am not telling you what to do with those money, but you should recognize that is extra blessing, not something you are entitled to.