At the risk of sounding like a bad mom, I did an ultra distance triathlon (swim 5k, bike 200k, run 50k) nine months post-partum. I did not incur any injuries. I was very involved in my daughter's life during that time (and still am). My husband and I are still married. :)
I did a lot of my long runs pushing a stroller, staring down at my daughter's sleeping face and stopping occasionally to nurse on the side of the trail. If she happened to wake up I would keep her happy by singing to her while I ran. I have a lot of great memories from that time and I like to think those runs were actually something of a bonding experience for the two of us.
I was still nursing at the time of the race so my husband met me at aid stations with my pump, with permission from the race director.
Of course, you will have a toddler as well as a newborn so that adds a new dimension!
Anyway, everyone's situation is different and I completely understand where the other women on this thread are coming from, and why they might recommend against it. Just wanted to let you know that it can be done - without divorce or injury and I think without traumatizing your children for life, although I guess that remains to be seen. :)
Jessica Kelley http://evergreenendurance.com