It is an absolutely possible reality not a dream. And actually I would say you have a better chance of finding a decent man than someone without children.
I know personally of three people one with 2 DCs, another with 6 (yes) and recently another friend of mine who has no less than 5 who have met the loves of their lives. The one with 6 DCs got married in February. The guy has no children of his own, runs his own business and can't do enough for her. My friend with 5 whose youngest is only 6 was adamant that she was through with men, but has met the love of her life. He was an acquaintance who had secretly been in love with her for years; he takes care of her and the children, buys them clothes, babysits, treats them like his own and tells her he can't live without her.
What all of my friends had in common was that they didn't try to actively seek men to make them happy. They put their children first, had standards and got on with life. I've talked to my dad about this, and he says that that men don't care about how many children a woman's got if they love them. It's about how they feel when they are with them.
None of my friends met their partners through clubbing etc. I personally don't think that these are the best places to find men with a mature outlook on life and responsibility. But who knows? The friend with 6 got into gardening and met her guy through that. The one with 2 DCs met her guy at the gym.
All you need is a positive attitude. You have an advantage over younger women in experience and knowing how to sustain a long-term relationship. You must look after yourself and your health and banish any negative traits like moaning over your situation etc. Smile and be open, and trusting. Men sense when a woman is still nursing hurt feelings from a previous relationship and run a mile.
If you meet any potential partners you should introduce him to your children straight away (as a friend) in a neutral public place, restaurant etc so he can see if he likes your children before getting involved and wasting your time.
Good luck!