OP, the only ones you are harming with your approach are you and your dcs.
My dm married a nasty, violent, racist misogynistic man, my f. Life with him was a misery until I escaped at 18. I never went back.
Like you, I will never trust a man, and never have a lasting intimate relationship. I can't help that, what's done is done. My dm didn't knowingly marry a creep. Blaming her now would be a bit like blaming a DV victim.
My dc have little relationship with their df and almost no contact with his family. But on the other hand, our life is full of such freedom and so many joys compared to my childhood.
We have a lovely home, a happy, cheerful, well fed, colourful relaxed home with music and fun. We travel and have holidays and treat each other with respect. Friends and family are welcome in our home. We have parties and small luxuries. I take huge pleasure in giving my dc the childhood I did not have. I regard us as genuinely lucky to have the life we do.
Why is having a resident man in your life so important? Does it matter? It is easy to have a great life without one. Why not focus on improving your life yourself, instead of waiting for some fictional man to come riding to your rescue. You are a much more reliable choice, and if such a man does eventually appear, well you will all be better off from your lone efforts.
Take care to enjoy the life you have now, with your children, today. x