If I want to file Chapter 13 and strip a second mortgage, does my spouse have to also file if her name is on the first mortgage but not the second?

If you desire to file a chapter 13 bankruptcy filing, whether or not your spouse is also required to file with you as to deal with the first and second mortgage that you are writing about depends upon if her name is on both of the loans or not. If her name is on one or both of the loans, she needs to file with you for the bankruptcy protection to get the relief that you want per your question.

However, for a more concrete answer, I suggest that you consult with a bankruptcy attorney regarding the greater specifics as to your current financial status.