Why does Walt not join in conversation between his wife and Skiff Miller

Answer: Because she was convincing Skiff Miller

Explanation:

As stated in the book, Mr. Walt's wife was extremely good at persuading people and getting to agree with her on mostly everything. So since she was doing a good job at convicing Skiff Miller to give them the dog, Walt didn't want to interfere because if he did, things would not go as expected.