I did this for a few months with a woman who was older as well. Her son was about 8 years old or so and she never let me meet him. We "dated" somewhat casually though.
At best she will always be a woman who was foolish enough to have a child outside of marriage, and that to me is the ultimate dealbreaker.
The ones that want to do the kid intro early are trouble.
OP, leave the poor woman alone. She is probably struggling and looking for some real stability in her life and you're likely lying to her and selling her interest for some sex. You're why men suck.
I don't agree w/ the out of marriage comment. This is not 1840. People have kids in many different situations nowadays.