I've changed my usual name for this. Am a regular poster.
I think your GP is being far too casual about it, tbh. I wonder whether this is either (a) because your GP is not that knowledgeable about trauma and mental health or (b) because you are so used to coping that you come across as much more highly functioning than you feel. Or of course both those things might apply.
FWIW I have a not dissimilar background, though my dc are older now, and I struggled a lot for ages because I come across as so lucid and functional that it was hard for professionals to see past that. You write very eloquently, but I wonder whether you have really communicated to your GP quite what a state you are in? From what you've posted here you are actively suicidal, have you made that clear to the GP?
You sound as if you need a lot more help than you're getting atm. I have coped well for years, but speaking from experience, once the wheels start coming off a coping strategy of just blocking it all out, things can get quite bad quite fast. You are entitled to proper help, though you may have to make a bit of a fuss to get it. Can you request to see a different GP? You could ask the reception staff whether any of the partners have a particular interest or experience in mental health? I would suggest that whoever you speak to you request a psychiatric referral as a matter of urgency to a psychiatrist who is experienced in dealing with trauma. IME if you tell them you're planning to kill yourself, they do start to sit up and take notice. On a purely practical level, if they have to admit you to hospital it will start to cost them serious money, particularly if you're a single parent, so they should be keen to avoid that.
The obvious help routes within the local NHS are: psychiatric referral (some psychiatrists are brilliant, some are useless, a good GP should have some ideas about who they'd like you to see); community mental health team (support in the community, maybe visits from a community psychiatric nurse); local mental health crisis team (out of hours support); local psychoanalytic psychotherapy services (proper psychotherapy does exist in the NHS though it may not be easy to access - some counsellors are great, but many are not, or are not experienced with trauma, so it's very hit and miss). The wrong type of counselling can be seriously re-traumatising. You are not in a good place atm to be part of the learning curve for this GP and this counsellor, so please do try and get help from more suitable services. As a last resort you can present at A&E, tell them you're suicidal and ask to see the duty psychiatrist, though obviously there's always a gamble on how good the person you see wll be.
There is proper sympathetic help available out there, and you deserve to get it, as does your daughter. If you're in the London area there is also the wonderful Maytree Respite Centre to which you can self-refer (for some reason I can't get their website to load atm, but they're in North London, and you can phone them on 020 7272 6863 or email on [email protected]
Please do reach out for some proper help.