What is the ruling on visiting and congratulating a woman in childbed who is born of zina or from a kafir man, if she is a relative?

Adultery is one of the major sins. Your relative who committed it should be advised to make sincere repentance to Allah, and to be shown the danger of sins and the virtue of repentance. One of the best ways to advise her is to visit her when needed. Abandoning her is not recommended except after exhausting all efforts in advising her and supplicating for her, because abandonment may not be effective. A balance must be struck between maintaining ties and abandoning. If it is in her best interest to maintain ties and visit, then do not cut off your relationship with her, because maintaining kinship ties is obligatory, and advising a Muslim is the foundation of religion.