I'm not sure if it is your background and culture, or your husband, that has made your thinking so entirely biased, and honestly, wrong. Please please try and let go of your preconceived and set ideas about marriage and parenthood, as they are not helping you.
Let me try unpick some your last statements::
The thing is, I need to make a choice and both choices are going to make me unhappy.There is no happy ending to it, is there?
This is not true - you have fixed ideas that being a single mother is bad and you will be unhappy - I can promise you there are very, very many single mothers in the world who are doing a brilliant job of raising their kids and are also happy.
Either learning how to live with a cheater and putting on smiley face (I don't have much self worth left anyway so can't lose that) or leaving him and being a single mum feeling like I disappointed my daughter by being selfish and taking away her Daddy.
You can't learn to live with a cheater. You will always be unhappy and this in turn will affect your daughter very negatively.
Your daughter will not be disappointed that you didn't ruin your life and hers by staying with a cheater. You are not being selfish. If you subject her to growing up in a sham of a marriage with a desperately unhappy mother, she will probably never forgive you later on. And you will have taught her that men can treat women like shit willingly, and she will probably repeat the same pattern.
I can hear how sad and scared you sound, and I really feel for you. But you need to put your big girl pants on, start listening to some of the advice on here, and drop some of your extreme bias against single parenthood.
If you really want your daughter to have a good life, you need to leave this ridiculous excuse for marriage, and put her first, rather than hiding behind your fear.