This is a particular sore point with me. I LOVE babies and small children. I do NOT love them in Shul. Your rabbi is out of line, IMO, though to be fair and dan l’kaf zechus, he may be doing so because his wife is seriously in need of sleep, and cannot take care of the baby then. Of course, the answer to that is that he should get her a baby nurse, mother’s helper, babysitter, etc. and absolutely NOT bring the baby with him. There is no excuse for disturbing people during davening.
I experience this every Shabbos and Yom Tov in Shul, and to be honest I am very resentful of the really inconsiderate moms who bring their ill-behaved (and who can blame them, they are little children, after all)and noisy offspring into the ladies’ section, effectively preventing me from being able to concentrate on my davening. Especially bad is when the little ones are eating nosh on Yom Kippur, or crawling under my seat, as has happened many times. When I actually said something to a mother, she berated ME in a very loud voice. All I did was say to her that I would very much appreciate it if she would ask her son to stop crawling under me. She proceeded to tell me that I wanted this to be a kid-unfriendly shul, and who do I think I am. She was also pregnant, so I refrained from answering her further.
When someone has such a mindset, there is no correcting the problem. When the ROV himself has the idea that it is OK to bring a baby into shul (and what about the dirty diapers???), then there is nothing you can say. I suggest the Shul Administration, if any, should gently tell the rabbi, this is not a good idea, and either offer to get him a babysitter for the davening time, so if the baby MUST be taken out of the house at that time, someone can watch the baby in the rabbi’s office or something, or demand that he keep the baby home.