Legal Question in Real Estate Law in California

It depends on whether you only have a first deed of trust on house B, or a first and second.

It is my understanding that the amount of the loan that is not paid off by the short sale is taxable.

Roach is wrong. It has nothing to do with whether you have one or two loans on house B. First, whether you can short sale is up to the bank. It is not a legal issue. Second, if the bank agrees to a short sale, you need to make sure that they agree to forgive any balance. If you do not get that in writing, then it will depend on whether the loan(s) on house B were "purchase money" loan(s), meaning they were used 100% to buy the property, were made at the time of the property purchase, were for your personal primary residence, and were never refinanced. If they will not agree to write off the balance and it is not a purchase money loan(s) situation, they can come after you for the balance. In that case you will need further advice on structuring a foreclosure so that it prevents them from coming after you. Lastly, as for taxes, there is a temporary moratorium on taxes on forgiven balances for personal residence short sales and foreclosures. You would need to check with a tax accountant to make sure it applies to you.