If my bank miscalculated the taxes on my second home and they are in fact 33% higher, what can i do?

1) If the new fees are the appropriate and correct ones, you will probably have to pay them. The reason for "probably" is that you should double check your closing and loan documentation--if you are paying at the correct tax rate and correct interest rate, it *may* be the case that the bank cannot increase the amount being escrowed so long as you are meeting the fundamental obligations. That's not likely--typically, banks have considerable  discretion to decide how much to escrow--but  it's worth checking. You can--and should--also ask for an explanation for the increase.

2) If the extra $350/month is what will break you and the increase is otherwise valid, don't wait until you get into trouble--talk with you bank, explain the situation, and see if anything can be worked out. They'd undoubtedly want the extra money, but they also don't want you to default or walk away from the home, leaving them with yet another foreclosed property in a continuing down real estate market.

3) If you can show that (i) you were given the lower figure in advance by the bank and (ii) that lower figure was a material, or important, factor in your buying the home--i.e. that you wouldn't have bought it at the higher figure--you may have grounds if necessary for a lawsuit against the bank on the basis that they made material representations which induced you to buy the home.