At this point, my head cannon is that she just lied or just a temporary contract with the dad... This mommy lesbean took the "Mommy" quite literally
They made a deal to get married. She could be a "model figure", take care of the girl and help her in the entertainment industry. And, at the same time and probably unknown by the father, spend time with the girl and maybe make her fall in love with her.
No, she didn't marry Tao tao father. Actually it's a fake marriage so Su-Man's parents won't nudging her about marriage.
Why did she marry her father