Is the wife considered sinful if her husband becomes angry with her and does not forgive her, despite her repeated apologies, because of her quarrel with his son from another mother?

The wife's apology should be accepted, and she should be shown affection. The husband does not have the right to be angry with her simply because she argued with his son, unless she was at fault. If his anger is not justified, she bears no sin. She should continue to try to appease him.