13 years of infidelity is a major pattern that shows a person has a big problem, whether it is morals, disappointment in the person she married, or what have you. Mine was a situational aberration.
I was in graduate school and my boyfriend, whom I loved dearly, was in a car accident that nearly killed him. He was out of school for a semester. During that time I found myself lonely and horny, and I succumbed to the temptation of another man. Maybe # 1 boyfriend and myself were "going steady" but we weren't married nor even engaged. In a lot of circles, what I did wouldn't even be a big deal since there were no promises spoken.
Well, someone ratted me out to the # 1 boyfriend and he tricked me into getting over his knee for what I thought would be a fun and erotic spanking. Instead he went beyond fun and gave me a punishment spanking I'd never agreed to, plus he ignored our safeword.
This didn't solve anything. It didn't convince me of his male dominance. I was hurt and angry and felt betrayed. Because I recognized I didn't have the moral high ground, I continued in the relationship and forgave him for his part in this fiasco.
He still had trouble forgiving me for being with someone else while he was at home recuperating. We stayed together another year and a half but then parted company. The rest of the relationship was loving and good but the issue of my single case of infidelity remained a problem until the end.
Good luck to you both, but if your second marriage succeeds it isn't because you spanked her. It might be because you so have become what she wants of you: a dominant man.