Is it incumbent upon the sister to sacrifice her husband, who commits fraud, manipulation, and adultery, especially since she is living with her father and has children, and given that he is on Hajj, making reconciliation between them difficult?

If your sister is financially able, then it is good for her to slaughter a sacrificial animal (udhiyah) on behalf of herself and her children. However, the sacrifice made by her father will suffice for her if he makes the sacrifice, as long as he is the one who provides for her; because the udhiyah suffices for a man and the members of his household whom he supports.