The two important fathers in The Kite Runner who have lost their wives are Baba, Amir's father, and Ali, who is believed to be Hasan's father. Both deal with their sons differently.
Ali is very loving towards Hasan. It comes out later that Ali is sterile, and Hasan is actually Baba's son, but Ali, grateful for the chance to raise a son at all, treats him with love:
Hassan's father, Ali, used to catch us and get mad, or as mad as someone as gentle as Ali could ever get. He would wag his finger and wave us down from the tree. He would take the mirror and tell us what his mother had told him, that the devil shone mirrors too, shone them to distract Muslims during prayer. "And he laughs while he does it," he always added, scowling at his son.
Ali's wife, who hated him for his disabilities, left soon after Hasan's birth, and Ali deals with his loss by loving Hasan as much as he can. He knows the truth about Hasan's father, but does not begrudge it, instead appreciating Hasan's mere existence with his words and actions.
Baba, on the other hand, is somewhat disappointed in Amir's introversion and interest in writing, and so treats him sternly; he wants his son to be strong and brave, and sees this in Hasan instead. Amir becomes jealous of Baba's clear love of Hasan, but he doesn't know that Baba has a real reason for the love:
How could I have been so blind? The signs had been there for me to see all along; they came flying back at me now: Baba hiring Dr. Kumar to fix Hassan’s harelip. Baba never missing Hassan's birthday. I remembered the day we were planting tulips, when I had asked Baba if he’d ever consider getting new servants. Hassan's not going anywhere, he'd barked. He's staying right here with us, where he belongs. This is his home and we're his family. He had wept, wept, when Ali announced he and Hassan were leaving us.
(Quotes: Hosseini, The Kite Runner, Google Books)
Baba's pride and his love for both his sons allows him to manifest different signs for each; he approves of Hasan with his actions while keeping silent about his fatherhood, but supports and loves Amir while teaching him strength through adversity.