Ohdear - No, you are not alone. A couple of months ago, I felt pretty much the same. When you feel like that, it doesn't matter how much someone tells you that you are needed, because you do not believe them. However, I will reiterate...your kids DO need you, but then you know that in your heart of hearts really, don't you?
I have been in your situation, but not a lone parent, and I cannot even begin to imagine how hard it must be to do that, as I find it hard enough with one child and both parents! You must have had to be an amazing person to do that by yourself.
I know that things seem like they will always be bad, and that you have had a horrible life. I never got on with my Mum, and found that counselling really helped me sort my head out with that situation. It is not the be all and end all, and it doesn't change the events that have happened. It merely helps you get 'closure' (in US-speak) and move on. Sometimes I still have down times when I ask dh 'why doesn't my mum want to be with me?' but they are the really low times, and most of the time I can accept that it is her problem, and nothing to do with me.
Try to take each day as it comes, and not to think too far ahead. The future always looks black if you look too far ahead, whereas you can deal with one day. DO NOT do anything to yourself, because that would be really sad for many people in your life. Don't think of it as easing your own pain, but more from the point of what it would do to your children. You WOULD be missed, and it would be a tragedy. Please accept it for now, even if you don't believe it.
Sending lots of hugs to you. Feel free to CAT me if you want, because I do know how you are feeling.