I think what you've got mixed up there is that the Booker that becomes Comstock never had the child, he hired the female Lutece to get him an heir of his own blood after he couldn't have a kid due to exposure to whatever it was Lutece was experimenting with. Lutece used a tear to get to the universe where Booker didn't get baptised and had a kid which is where she met her alternate self in the male Lutece.
You sell your daughter to pay for debts, then for the next 20 years you lock yourself away in depression then you meet the lucea twins and after setting up Columbia they create the tear technology. As your a bit nuts by this point the twins use the tears to travel back in to an alternate reality to hire you to then go save your daughter and he frames it as paying for debts by saving her. And it all stems back to being baptized because in the reality where you are baptized you become a religious zealot, but in the version where not baptized you go on to be hired by the twins. Thats the basics right ?
I think... love it when a story makes you do that.
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