My father expired as my wife went off to her home and not showing my only sin.. what legal action can i take against her?

Issue notice to her to restitution of conjugal rights ,filing petition in court or family court.

As per your query

Under section 9 of the Hindu Marriage Act, a spouse has left the other without any reasonable excuse to return. An aggrieved party may apply for restitution of the conjugal rights whereas a legal notice is to be served to the other party and after the court passed a decree for restitution of conjugal rights

However, there is another way out, if the decree of conjugal rights is not honoured for more than one year after the date of the decree, then it becomes the ground for divorce. In this case, the aggrieved party may directly request divorce before the court.
Hope it clarifies the issues!
Regards
Minakshi Bindhani