lenamechange, I'm in a similar situation...
Me: 44, two kids, two divorces (both kids from second marriage). Had been separated nearly 2 years when I met DP, and was happily single (but divorce was underway and is STILL not absolute yet due to ongoing financial issues)
Him: 46, one divorce, one child from live-in relationship. His DD was under 2yo when we met. His exP is a nutter (eg see my thread in Legal about harassment). DP wishes he had not got involved with her, or had stayed away when he left her instead of going back (she subsequently had his child, which prolonged the painful ending of their relationship). He hates that her behaviour has an impact on my life. He has had to go to court to secure contact with his child. He is still trying to sort out joint finances with her.
He and I met through a dating site in Nov 2010. He is my soulmate, my other half, the love of my life...I could go on! We are absolutely and completely right for each other. We both made poor choices in the past (my first exH was physically abusive, the second I was never in love with and the relationship became emotionally abusive). The past is exactly that, and we aim not to let it impact negatively upon the present.
Sometimes I think his anxiety or reaction to something is a result of his previous experiences. He once said something innocuous to me that I completely over-reacted to, as it was too familiar and something my exH had said, though with different intentions. Generally though, we are extremely compatible, good at resolving our (rare) differences, agree that regular communication and honesty are essential and cherish each other, showing respect at all times. I cannot imagine my life without him, my DC adore him (when he comes round it's a race to the front door for the first cuddle - mostly I win!) and he says he has never been more content than he is now.
Others would see red flags in what I have written. He invited me to Dubai only four weeks after we had met and we spent new year there, having met less than five weeks earlier. On New Years Eve we said 'I love you' to each other for the first time. Both of those events are 'red flags' to some. Nearly 18m from our first date, though, and I am 100% sure that I have met the man I will spend the rest of my life with, and he says the same about me.
Just to finish off, my parents like him too! More than they ever liked either of my exHs, in fact...
Good luck with whatever you decide. Sometimes good men have a less than ideal history...and so do good women!