I still don't think the route to help for Khimaira is via the GP. Not sure of others experiences of GPs but nationally most practices are under deluge from increasing numbers of patients. Even if someone is experiencing mild to moderate depression and anxiety, they are only going to be prescribed ADs and I think Kh you are saying you don't feel depressed - have I got that right?
I agree though that you could maybe benefit from more therapy although you say that it was more or less forced upon you when you were at Uni, although it seems it was some help, as you asked for help with managing your children. I don't know if it's a typo but you say he said you had no self esteem and I'm thinking he maybe said low self esteem, which is what "jumps out" in all your posts. The reason is clear when you talk of how it seems you were never "good enough" for you parents and were being compared to your siblings, and "missing out" in the comparison.
Unfortunately the parental "messages" we get as children (in your case "you aren't good enough") stay with us and whir in our heads like tape recordings, though sometimes we are not consciously recalling these things, but they will be there buried in our sub-conscious. Maybe this is what the therapist is perceiving as trauma, I don't know.
I don't know your financial situation (and assume you are a single parent?) but IF you can afford therapy the place to look is the BCAP website (British Counsellors and Therapists) as they will be registered practitioners. Mind they charge around £50 an hour dependent on where you live. I honestly don't think the GP would refer you for counselling, and even if they do, it's usually 6 sessions of CBT (cognitive behaviour therapy) which is a therapy based in the "here and now" and the aim is to help people replace negative thoughts with more balanced ones. Sometimes we get negative thoughts spiralling down and down and can't break out of them, which of course makes matters worse. There are loads of books at a reasonable price on Amazon on CBT, so maybe you could have a look to see if it's something that might be useful.
We can't change our past or the "messages" we were given, but we can modify the effect they have upon us in our adult life.
Do you have any RL support, family/friends? Sounds like you can't control your eldest child's behaviour, and again there are many books that can help, and TV programmes but you need to be motivated to do this. You are obviously a bright woman as you went to Uni, - what is your specialist subject (oh sorry sounds like what they say on MasterMInd!)
I didn't go to Uni and I had some very destructive "messages" from teachers at school, that stayed with me for many years. I passed the 11 plus (in the 1950s when everyone took it I think) but only about 10% of children passed, and I went to grammar school. It turned out to be quite the wrong school for me, as I was amongst girls who had mostly come from private schools and were much cleverer than me and more confident. Also they were mostly middle class or what we thought of then as "posh" and spoke differently to me. I came from a respectable working class family but once I had been to parties at their houses, I never invited anyone back to our humble semi!
I left before I took "O" levels and the awful teachers or "mistresses" as they were called (nearly all spinsters) told me I had wasted a place that another girl could have benefitted from and I would never "make anything" of my life. This stayed with me for many years and I followed my sisters into a commercial college and worked in offices for some years. When I was 37 and more confident I applied for a place on a social work course and got a place, and qualified. I worked for the same LA for some 30 years, as a social worker and middle manager and loved every day of my job and finally threw off those messages. SORRY I don't know what's got into me, I don't usually do this. It comes from learning to touch type at that commercial college!!