I often find myself feeling the same way as you describe your wife's feelings. I have three kids, the oldest one is 5. I also feel overwhelmed and exhausted by my "mom voice" and there are days when I feel nothing can snap me out of it. It's hard to be needed 24 hours a day.

Does your wife work? Or exercise in a group? I found having appointments outside the house to he helpful when I had post partum depression.

One point that I would find concerning is that your wife doesn't want to do anything about it. That's really too bad. Counseling could help her identify triggers and help come up with strategies to cope. Having young kids is really hard and I know a lot of couples in the same position you are. Before our third child, I would say us included. I doubt it will magically get better when your kids are older.

What helps me is exercise, writing in a journal and having time occasionally to do whatever I want without needing to check with someone if it's OK. It might sound trivial (or sad) but I love going into the city alone for a few hours even if I don't accomplish anything. Just having the freedom to choose which direction I go in for once can make a big difference.

When I was really struggling with PPD, this helped me https://www.motherhoodandmore.com/sometimes-i-cry/