OP I think that is a great idea. We (DH and I) grew up in a more social and more academic area, so we are accustomed to people being more down to earth. When we moved here, we found people very insular and did not see any sincere reaching out. There seems much more of a pissing contest here that no one admits to! We find it funny.
Most people we know who grew up here (about half our friends) have no friends here, and we had no idea why. We learned (f those friends it just so happens) they would rather spend time with their family. After all these years they have not really moved far from their birth family. We found this odd in this day and age. Then we thought what a shame, they are missing so much!
You can still be close to your family and have friends, right? The bonus is that you get free child care when you want it. (You do realize what a big deal this is for those of us who do not have family nearby right? But I digress.) As long as you are a good friend and neighbor, there is no reason why there should not be a mom network in your own neighborhood!
Make some flyers, serve some coffee, and enjoy. We would love to have such good, decent neighbors with good intentions (and actions to back it up). We are stuck in an antisocial "must not wave - yet nosy as can be" community, unfortunately. The neighbors will stare right at you, but refuse to wave back. This is something else that has become amusing to us!
Where are the good neighbors?
I wish you good neighbors OP. You can't buy that