Hello. My name is XXXXX XXXXX I will be happy to answer your question.
I am sorry to hear about this unfortunate situation that you are in.
There is legal presumption that both biological parents
have a 50/50 right to equally share timesharing and custody of the child, however this presumption can be rebutted in court.
Unfortunately, as long as, there would be no imminent danger to your three minor children if they were to visit with the mother
and the man she is living with or some other evidence that it would not be safe for the minor children to stay with the mother, the judge can order joint custody
and also is more than likely to grant generous visitation to the mother (provided that both of you agree that you would have the residential custody of all children).
So in most cases it is better to try to agree on custody / visitation with your spouse, rather than leave it up to the judge to decide on how to establish custody / visitation, which in many cases not only lengthy and expensive process, but also the results can be worst than if the parents were to come to an agreement on child custody / visitation on their own.
Also, at this point it is really important for you to consult and retain an experienced local family law
attorney, who would be able to fully protect your legal and parental rights
in your upcoming divorce.
I wish you the best of luck!