All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
This woman committed a grave sin when she abandoned her husband and had an illegitimate relationship with another man. So, she must repent to Allaah fulfilling the conditions of repentance mentioned in Fatwa 86527.
As for marrying that man after her husband had divorced her and her ‘Iddah expired and that man embraced Islam, it is permissible according to the majority of scholars if it was done after they had both repented to Allaah and their marriage met the conditions and requirements mentioned in Fatwa 83629.
As for cutting your relations with her, in principle it is not permissible for the Muslim to desert and shun his relative except for a religious reason. If this woman has repented of the sin she committed, then you are not permitted to desert her because repentance wipes out the sins that were committed before it.
On the other hand, if she did not repent, then you should look at what benefits her. In other words, if deserting her helps in deterring her and is hoped to change her to a better state, you should desert her. But, if keeping relations with her while giving her advice is better for her, you should keep relations with her while enjoining good on her and forbidding her from evil. For further information, see Fataawa 118474 and 86090.
Allaah Knows best.