Is a father considered sinful if his sons do not care for their half-sister, despite his continuous attempts to encourage them, and does this justify him boycotting them as a means to mend the relationship?

Maintaining kinship ties has degrees, the lowest of which is avoiding severance, even if only by greeting. As long as the children do not cut ties with their sister, there is no sin upon them, nor upon the father. The father should advise them about the virtue of maintaining kinship ties. And the children should obey their father by maintaining ties with their sister and being good to her; this is out of dutifulness to their father and for the sake of their kinship ties, for maintaining kinship ties is a cause for an increase in provision and a delay in one's appointed time.