Is it permissible for me to visit my husband's brother's wife in her home and congratulate her on her holiday, knowing that she is Coptic, and I fear that not visiting her will lead to a rupture in family ties?

Congratulating Christians on their religious holidays is forbidden. However, congratulating them on matters shared by all people, such as marriage, childbirth, recovery from illness, and the return of a traveler, is permissible. If visiting the woman on her holiday will lead to congratulating her on her holiday, then she should excuse herself and not go. The good relationship with her should be utilized to invite her to Islam with wisdom and beautiful admonition, as this is the greatest kindness to them.