Wow, you are so much nicer than I would have been. I can't believe anybody would expect a 6 week Newby to be left at home...My brother and SIL had a no kids rule which was fine as it's their day and we were happy to organise babysitters months in advance and let them know that we would just have a 6week old with us. Then we got a text less than two weeks out from the wedding tell us that no babies allowed as they will cry loudly and ruin the video they were getting done which they were paying a lot of money for.
So...we thought about it before replying, then politely said that unfortunately we would not be able to attend (we also had to travel to get there). This of course caused unrest and so we went out of our way to go up and DH stayed with bubs while I attended the ceremony as bub wasn't allowed to put foot on the sand - ceremony took place on a windy beach (so the speakers were all crackly), beach goers everywhere, noise, boats, etc.
We then turned around and drove home, only to have to drive back again with our children the next day to please close family who had also driven a long way and were put out because they didn't get to see our kids.
And after all this, my brother and SIL were so ungrateful and didn't talk to us for a year. Their spin on it was that I should have been grateful to have been allowed to attend the ceremong still - what the? Meanwhile, we said nothing of it negatively to our family. I have no idea what others said to them though - I'd say this is probably what caused the problems.
So...after all that - I would recommend if you want both spouses there, then babes in arms be allowed, or do not get offended if they decline if you allow no babies. (If they are fed and cared for, I doubt they will interrupt, and even if they start getting grisly, if they have caring parents, then I'm sure they will go and pop them down for a rest, etc. when needed.
I think it's quite acceptable to have no kids at a wedding. Just as pp said - make out the invites specifically and also pop a note into the envelope or phone people to make sure they have made arrangements. I remember being 14 and not going to a cousin's wedding and an aunts wedding as I was considered a child - and it was fine. As long as there is consistency no one will be put out. Hope you have a lovely day and the whole kid thing goes smoothly for you.