I would like to answer this post because I too have been a single mom of a now 11 year old son for almost 5 years myself. I mean, I dated here and there, but nothing serious and nothing real. And, like you, there were many things that didn't work out. So, I decided to let go and let GOD. And I did no searching for my current mate. He found me. "A man that finds a wife finds a good thing." The Word of God does not mention the opposite. Before my man and I met, I was living for God. Going to school, being a full time mom, working from home more. Spending time with my parents and other loved ones. I had already prayed and let God know that I'd like to be married one day (maybe a little over a year ago). But, I knew with that prayer, I had to have faith. And that faith said that if God decided to allow someone in my heart or not, He is still God and I love Him always. But my man came up to me from behind. And from far off away, he was talking to me, but I didn't hear him. So he repeated himself....and it went from there. It was cute, kind of funny even. Before I met him, I tried the dating sites too. I also thought about speed dating and other unconventional methods. But something in my spirit kept telling me those are not ways for me to get a mate. And the verse "God made woman for man" also stuck out, so I quit thinking about it so much and did what I felt God wanted me to do.
So, this is my encouragement to you: give your heart, your life to God. And if He sees fit, then He will allow the man to find you (wife) and go from there. I will say this: with the man I'm with now, we started things off quickly, but we are building a healthy relationship and we do pretty good together. But, I would have preferred to date him for a short while and got to know him a little better before becoming intimate. I say this because emotions get in the way of practicality sometimes, and it's hard to slow that down when I feel pressured (BTW, he's older in physical age than I am, so that also plays a part in this)But the good thing is he accepted my son with me when we met. But I will admit, I feel hurt, maybe jealousy from time to time because time has to be split. And being mom and lady, I have to seek a middle ground. It's not easy, but because acceptance and more so committment are already there, then it will work.
With that said, I would advise this: Pray about it. God gives you the desires of your heart. Talk to Him and let Him take care of it. But in the meantiime, enjoy the special bond you have with your children. Because when a man comes into you life, things DO change drastically. And in the meantime, God may be working to prepare you for the changes that come with dating/marriage. May God bless you and your family