Poppa, while I understand and can even appreciate your thought process, you are holding that process at the expense of other mispallelim who cannot concentrate while kids are running around during the time that they cannot reasonably sit and daven. I think it is wonderful to expose kids to shul, but not on the plaitzes of other people.
I stayed home for several years until my youngest child was old enough to go to Shabbos davening groups. There was many a great drasha that I missed, not to mention my father O”H davening for the omud before he was niftar, when my parents spent a Shabbos or Yom tov with us. Disruptive kids do not belong in Shul, no matter how much you would like it to be a good idea for chinuch. Unless someone is there to remove them the second they become “squirmy,” it is not derech eretzdig to everyone else OR to kovod Harav and more important, Kovod haTorah.