Your children need you - I was 36 when my dad died - im 42 now and it is still affecting me. I miss him every single day :( My life would be better if he were still around, even thought i didn't "need" him for day to day stuff.
You say your children are independant - do you not realise that this is because despite what you think, you have given them the tools to be that! OK, so you have been ill, lots of parents are ill in lots of ways and maybe cannot do all the lists of things a "good" parent is supposed to do. If you were as crap as you think you are,, your children actually wouldn't be so independent and would be struggling so you should be proud that you have three resiliant and independent children. As a mother, that is all i want for mine - and of course happiness.
Your illness is distorting the way you see yourself - you are not seeing the real you, you are seeing someone that you don't like. Everyone needs someone to "blame" when things are bad, but you are blaming yourself and it isn't fair.
If you take your own life you are sentencing your children to a lifetime of unhappiness thinking that you didn't love them enough to say - they wont think, "mum did this for us because we needed to be children" they just want their mum. Also, history repeats itself - my cousin commited suicide his ten year old boy found him along with his uncle (my cousins younger brother). The affects this had on the whole family were devestating - The son has had several failed suicide attempts and stays in hospital after a series of breakdowns. The brother, well he is dead now after living a terrible life, unable to control his temper and pretty much became a sociopath - he died from a herion overdose, aged 38, and so it goes on.........his children are struggling now to come to terms with this. Maybe, just maybe if my cousin thought about the future when things were so black for him that day he felt he couldnt continue, if he realised how many people loved and needed him, he wouldn't have done it. "help" was less forthcoming in those days, maybe now he would be been in a position to seek help and things would have been so so different. You do not want your children to have to come and put flowers on your grave, you do not want your children to only be able to dsecribe their grandmother - you want to see those children become the adults that you have made into such independent folk, you want to see them nuture their children and i be there for them when they are struggling, you can tell them the things you did to cope.
Sending you love and hugs, be strong, you can get through this, for your children, but most of all, for you xxx