Hate to tell you, sweetie, but the reason that the Brady Bunch is NOT a fantasy is because both Mike and Carol HAD kids. The tone of your email suggests that because I am a single guy who found love with a childless woman that my advice is invalid to you. Everyone likes to think her situation is particularly unique. Advice for women over 50 is almost identical to advice for women under 50.
There is no rule that states single moms must end up with a man or a woman with kids.
If your kids are young, just imagine how many years you'll be out of the dating scene before they leave home. Don't expect your kids to be overjoyed when you first start dating. Explain that you love them, but you also like to spend time with your friends (just like they do). And as the adult, you get to make the decisions and not your kids. But they shouldn't be the main topic of conversation during your date.
If you feel ready to date, there is no reason to wait for the perfect time or until the nest is empty. After all, they have had you to themselves for quite a while, and now they have to share. Take some time to find out about this new man; his interests, work, and hobbies. Children get uncomfortable when there's a parade of men taking their Mom out.
In actuality, many childless singles find single moms very attractive as they can, in a lot of ways, be more mature and independent than a young, developing woman. If he is a guy that has never dated a single mom before, chances are he is going to hit a serious learning curve early on in the relationship.
My family believes this woman is out to get me, and that I don't need someone twice-married and 16 years older. You need to make sure that a long-term relationship could stand on solid ground.
I tell them we get along well and I enjoy her kids very much. Which means you have lots of information-gathering to do.
You should be talking to your girlfriend about her past. If she's blaming her exes, view it as a danger sign; it means you'll be the next target.
If she has no insight into her own contribution to failure, or refuses to talk about her past, then get out now.
And by the way, how long did she wait between ending each marriage and starting a new relationship?