I asked her how was lunch, where did they go, what did she eat, etc.
That would feel like grilling to me too under the circumstances...
Your motives are showing.
The only way she will know that you get how serious she is would be to mean it. I think that her mental health is a huge issue. Do you think she'll snap out of it? She could still have PPD. When you are ready to take a chance and have some movement, I would push the issue and frame it as for the benefit of her kids. They should not be stuck living with a depressed mother.
Seriously, if you have to D and compel her to get help, that may be what has to happen.
Again, I can't say for you, I am just working with what you've shared with us (see, the DB squabbles have made me gun-shy).