The stepson's extreme distress is heartbreaking, and the puppy clearly provides immense comfort. While the wife's initial anger is understandable, her stubbornness is causing severe emotional harm to her child. The husband is simply trying to alleviate his stepson's suffering and preserve family peace, not undermine his wife.
The husband is prioritizing the fleeting happiness of a child over his marital commitment. The wife's boundaries were crossed by the ex, and the husband's lack of support undermines her authority as a parent. He's creating a rift in the marriage by siding with the child's emotional whims and enabling the ex's manipulative behavior.
The wife's reaction, while initially justified due to the ex's overreach, has become disproportionate to the situation. The stepson's distress is significant, and the husband's concern is valid. However, he must also acknowledge and respect his wife's feelings of being undermined. A compromise, such as supervised visits with the puppy, should be explored.