You can be a father like that with the nanny, and you are fully capable of taking care of your 1 1 year-old son!
Tell your father clearly: you have committed bigamy! Knowing that the other person has a spouse but lives like a husband and wife = bigamy!
No matter how stubborn they are, they are eligible to report their "bigamy" to the procuratorate!
For the benefit of your family, you should resolutely "put righteousness above family members"! Otherwise, when you are blackmailed by the other husband, the result will be even worse!
I hope your father understands the righteousness and resolutely disowns the married woman. If he meets the conditions for remarriage, he can find another legal spouse. You will definitely support your father's legal remarriage.