Yep, you skipped a dialogue. He did tell Walter how his mother died, but only on Day 11. I won't tell how his mother died since it is a bit heavy of a topic.
Thank you again! I finally got the answer after replay the whole route again!!! I didn't get it on my first playthrough ( perhaps the relationship points too low) but walter still know how did coach's mother pass away so I was confused. Maybe writing mistake!