First time here and I'm on mobile so forgive a few of my grammer mistakes.

Long story short my wife had an affair at her sister's bachelorette party and got pregnant with OM's child. Found out a year ago when she gave birth to a child that's clearly not mine (I'm black, she's white) since OC was fully Caucasian with blonde hair. Of course I got mad, told my family who shunned her, and told her family who did similar. Right now the OC is 1 year old but I can't STAND having them in the house. We already moved to another area to avoid the fallout but she simply keeps begging me to not divorce her. We have twins (5 years old) together and she's insist on raising the OC. My ultimatum to her was to give the child up for an open adoption (where she sees the kid sometimes), one of her relatives (grandparents), or give full custody to the OM (she outed him and he's willing). I keep telling my wife I will not raise OC and she's accepted that she will have to do everything (financially and care wise) for OC but I feel like its driving a wedge between her and me and the twins. I understand that Dr. Farley's advice is to raise OC's but really why should I?! How do I explain away a stepchild that looks NOTHING like me and is younger than the twins I had with my wife? Please help smh, it seems like every alternative will end up making her resent me.