(1) I'll spare you yet another hypothetical family budget monthly itemization.
(2) I'll concede that it is clearly possible to raise a family in New York on $110k/yr.
(3) I'll assert again that it is not comfortable to raise a family in New York on $110k/yr, nor does it appear to be easy.
There are obviously a lot of sacrifices you can make to make the budget work out, but in a family scenario, not all sacrifices are tenable.