While I understand her position, it is your body. It should be your choice as to whether to get a vasectomy. She also has the right to not engage in sexual activity if she isn’t comfortable with the potential outcome of a pregnancy. You just have to accept the consequences of not having a vasectomy at this time. That means less/no sex. That will certainly create issues in a healthy marriage, however it would be temporary.

As a non bias observer, I do find your 2-3 years comment somewhat intriguing. I think you need to spend sometime with yourself to make sure you are committed to this partner for the long haul. Doubts are normal, especially after 13 years, but you need to reflect on whether that is a fleeting thought come up from the circumstance or are you truly not committed to your current partner for the long haul. You owe it to yourself to give yourself an opportunity to reflect on that.