Marty, I'm sorry but I missed how old your kids are exactly?
Geez, this brings me back to when I found out my mom was dating again. I was 14. She 'hid' it for a good while, so I was asking 'where are going? who are you with?' Y'know, I was 14, a little paranoid, and didn't like being left out of the loop. I still remember the day she brought my future step-dad home. Poor guy! The circumstances were different than your though. As an adult, it is hard to say if mom did it the best way or not. That takes a lot of hard discretion to figure out the particularities of what to share with your kids, and what not to and when?! She did what she figured was best at that time, and it all seemed to turn out ok in the end...so.
Anyways, I don't really have a point to that story.

Except to say: I surely know my mom was
not looking for the love of her life at that point, she was originally out to have fun. Later I found out that she had dated many men before meeting stepdad (never knew about it at the time). But it worked out that they were great together. He knew about us (myself and my brother) and he was divorced/had grown kids of his own. He even liked us. haha. That's pretty good considering how I was at that time.
Worrying about
if there are men who will love you and your kids almost seems silly to me. Because of course there is someone in the world who will be right for you! In your 40's and with kids who aren't little ones, it is a whole different ballgame than if you were a 22 yr old single mom.
Your kids have a father and a family. They have already been 'raised' to a large extent. Somehow that makes a huge difference, I think.
And so long as you are there for them as a mom, hearing how great your kids are and how well they seem to be: they'll be able to handle your dating however you do choose to handle it with them.
It really helped when I could speak to my mom honestly about the situation, though. I mean, knowing she was seeing a man and being able to voice my concerns/feelings about my father in relationship to it all. We grew closer and got along a lot better at that point. But it all depends so much...
All in all, I agree with Noddy and Stuh. And I wouldn't waste time dating men who aren't cool with your kids (knowing you have kids). Because you never know who you will fall in love with or who will be the one for you!
good wishes