I also do not think that forgetting is possible - you cannot unknow what you know actually happened. Forgiving is possible if you can come to understand that your Mother was (for whatever reason or just because she was made that way) unable to be the loving mother you yearned for. Eventually you may feel desperately sorry for her because of the happiness and joy in her family that she never experienced.
'Moving on' is not dependent on forgiving or forgetting but rather on developing an appreciation of and joy in, the here and now. Because of, in part, your past I am certain that you will have have ensured that there is a loving, caring relationship with your own children. There is a wee 'trick' which I learned during Counsellor training which most certainly worked for me. It is to find some photographs of yourself as a young child and look at them with fresh eyes as if YOU were the parent of that young girl. Is she loveable? Does your heart go out to her? Do you wish she was here so that you could hug her and look after her? Well you can, for that wee girl is inside you, she is your inner child and you can mother her and give her all the love she missed out on in her early life. You will know what she longed for back then and your adult self, perhaps with help from your family, can supply that, be it praise for something well done, wee treats, a special birthday cake, a curly perm, whatever.
Sounds a bit airy-fairy maybe, but believe me, nurturing and loving THAT child can fill up that emptiness in your own, here and now, heart.