Hehe, this is such a perennial.
OP, this is what happened to me
In precis, I have a six month old and was in the same situation, except I had already booked flights to New York for the wedding. The bride made my infant an increasingly divisive issue, and it all ended in tears. In retrospect, I should have put my foot down earlier and not accepted silly compromises.
(and a still incandescent DH continues
It seems increasingly clear that brides in the West are becoming no better than spoilt toddlers having a tantrum in a supermarket. This is not surprising, because this is the age when many brides seem to have started planning their weddings. The childish spoilt, solipsistic, selfish attitude floated with her in an intact "my perfect day" bubble, even as she otherwise matured and grew. It's not a surprise, then, that they don't want other babies at their wedding. One big baby in a meringue is enough.
Many decadent brides have forgotten that weddings are not solely the "WORSHIP THE BRIDE SHOW" but should be a communal celebration of the decision the couple have made; in a very important sense, the wedding is for the benefit of one's community, not simply a forum for a bride to act out the fantasies she had as a 3-year-old playing dress-up. It is "your day, hun", but if you take this to the extreme, one is missing the point entirely.
If one cannot appreciate that the wedding is primarily for your family and friends, and that your primary duty is to make them welcome and happy in celebration, then one should probably not bother having a wedding and go on holiday to some nice island instead and pay some actors there to worship one as a goddess for a day. It'd be cheaper, and the food'll probably be better.
A wedding is different from a marriage. A marriage is between you and your spouse. A wedding is between you and your social circles. It should celebrate optimism, society, commitment and the shared interests of all the generations. It affirms a hopeful future to be shared with your conjoined friends and family and their children. A wedding without a babble of babies is a sadder occasion, and if your bridezilla friend doesn't realise this, I suggest you accept your "de-invitation" and hope that your absence might act as a pin to prick her ghastly bubble.
If it doesn't, good riddance to her - at least until she's completed her tawdry fantasy and has become sane again.