Can't comment on American "system" as I don't live in America.
You said: "Widowed with children at a young age, and watching my little ones, I realized that a man offers something to children that I never could; something more than a paycheck; an essence, an inner something that I lacked and they needed."
You are half right there. I was married 20 years in such circumstances, providing not only a paycheck, but love for the children as well. As it is clear now, we married for wrong reasons. Children grew up and moved on. There was nothing left for the marriage to survive.
She is now "happy" grandma, "children" had the love and have now children of their own, and I have memories.......................