Wow. Intense thread.
My advice would be what you originally considered: tell her exactly how you feel. Just like we grow and learn from our therapists, I believe our therapists also grow and learn from us. If she can learn from her mistakes with you, it may help one of her other suicidal patients somewhere down the line.
I have had SI, depression and intense feelings of loneliness countless times beginning in my pre-teens (I'm now 41.) I am in no way cured, but I've learned something in the past couple of years, which, when practiced, has changed my life immensely for the better. (I'm not suggesting rehab or recovery here, just leading up to a lesson I learned, so hear me out.)
In 2011, I went into rehab and stopped using drugs and alcohol, which I had been abusing since around nine years old. It was incredibly difficult, and was made worse by the fact that I was penniless, jobless and essentially homeless as a result of both years of rampant substance abuse and my worsening mental illness. I got a sponsor (like a mentor) who kept insisting I help others who were new in recovery and who had had similar experiences.
At first, I was super annoyed. How could telling my story and helping others get me a job, a place to live, or calm the demons in my mind? I hated her for her constant persistence in the concept. But eventually, I became so desperate, I was willing to try anything. So I started to talking to other women, sharing my story in meetings and at rehabs and in hospitals. If I saw someone new or crying or afraid to talk to others, I approached them and asked them out for coffee, gave them my number and became honest and open about my experiences. As I saw them slowly grasp onto a sliver of hope, then begin to smile once in a while, and open up to others, I began "getting out of my own head." I concentrated on using my pain and experiences to help these women.
It wasn't a constant. I often slipped back into depression and isolation, but held onto the concept, and in psych hospitals where I eventually met others with PTSD, I found myself talking to the shyest, loneliest, down-trodden women, some of whom had stories worse than mine. I heard stories that chilled me to the bone.
Now, I am often approached, called, and messaged by women who say I was a crucial part of their healing process. It made me realize I have a purpose, perhaps the most important purpose someone can have, if I practice it. It hasn't cured me by any means.
Right now, I am in a lonely, depressed spiral of isolation and despair. I don't have the energy or confidence to approach anyone. I am again one of those people who need saving. But I do have a network that is there if I am willing and ready to reach out. Some I met on sites like this one, some I met in hospitals who returned to their homes hundreds of miles away with whom I keep in touch online, and some I can see in person if I choose to. It really is two or three steps forward, one step back.
My very best friend, who was more of a sister to me, committed suicide in 2011. I have never gotten over it. But she felt the same way you do, that we'd all be better off without her. Her suicide destroyed her family and almost caused my own attempt. Also, my mother, with whom I had a loving, but difficult relationship, died when I was young. It propelled me into an adolescence of self-destruction, abusive relationships, and guilt that I still work on today in therapy.
Please believe me when I say your children will suffer well into adulthood with your decision to kill yourself. They will, however, learn how to be strong and follow your example when faced with their own inevitable adversities in their own lives, if they see you doing everything in your power to get well.
I hope you find even a sliver of value and hope in my story. I know that just writing it down, has done the same for me.