First of all, congratulations!!
I couldn't ride at all for years. I had to take a break from cycling. It's less up to us as parents and more up to the child's temperament. They don't often conform to what we want, especially as babes in arms. The funny thing was that I had planned all this stuff and it just went out the window the moment I became a mother. She had other plans. All for the better... being a mom is eleventy times better than any bicycle.
I wouldn't ride with a small child, anyway, as mentioned above. Their necks are so, so weak for the first few years. Even a mild jolt could cause problems.
I will say that we ascribe to the rearing philosophy of Attachment Parenting, which has proven to be very successful for our now 11 year old. Without a doubt, that had an influence on my activities, including riding.
Best of luck!
The bicycle has done more for the emancipation of women than anything else in the world. ~ Susan B. Anthony