It sounds like she is definitely lashing out at something you have said.....or somebody has inplanted the idea that's what you want her to do.
If you are in house separation, why would she care what you want from her? She was not doing those things that mothers usually do for their kids...when you were living in separated houses. So, she is blaming you for her not feeling like doing anything?
Well, I think it may be more than depression. Something led her to feel this way. I think it may stem back to that C who said she couldn't see you b/c it would be a conflict of interest. I have never heard of that with counselors. Something smells fishy there. Didn't things get much worse afterwards?
If it was not something going on from the C, it could well be somebody else's bad influence on her. Could be almost anyone, even someone you don't know.
It could be her hormones, if she mentioned she would go see a doctor. But something changed her mind. It doesn't mean she's getting ready for menopause, necessarily, but her hormones may need some help. I don't anything that can affect female the way messed up hormones does.
The other thought I have, based on the timing of event you have given, she may have gotten emotionally involved with another person. That would answer her wanting you out and her not being there for the kids. Then if the EA ended, it would account for her angry depression. Also would make sense of why she's was lying.
I'm not trying to plant any one particular idea in your mind, but since you have told us what she's been saying, I do think it's more than just "sad" depression. She wants to blame you for her decision to do nothing.
I think you should tell your son that she is depressed and it's not him. The "staying out of their R" is directed more about other things. Like if she was wayward and the kids weren't doing what she told them, etc. If she was wanting to D b/c there was OM and she was telling kids that both of you wanting a D? Then you would not step in to try to repair the damage in her R with the kids. She would need to do it.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!