Aryeh, he may be bringing the child to shul because his wife needs help (I don’t know what the situation is – do they have multiple kids? etc).
Perhaps the best thing to do is find some women who would volunteer to watch the child during davening with the premise of chesed rather than annoyance.
In my shul (a moderate size shul in a large Jewish community), kids are welcome if they are quiet. Generally, parents bring pacifiers or something if the kid is in shul, to keep them quiet. I come at the end of shul so that my son (who is over 1 year) can be quiet for about ten minutes and thats it.
One problem with bringing little kids to shul – if they are formula fed, I think if they are in diapers and will possibly soil themselves, they are NOT allowed in shul.