I get it that (as in so many other contexts) it's tempting to try to reach for an objective rule or standard. But I agree with those who have said that there is no reason to declare the wedding "child free" or invite all or none of your guests to bring their children. Many families and communities, including mine, usually invite children who are relatives, but few if any of other guests' children.
I can see it being a problem to, say, invite your brother's children but not your sister's, or all the children on the bride's side and none on the groom's. But that's no different from the general wisdom of inviting all or none (or very few) of a given category -- first cousins, club members, five out of six siblings, etc.
And I personally put nursing newborns who can't yet be apart from Mom in a separate category. We've never had any problem with that. But that's just because I think it raises different issues, not because I think there is any greater obligation to include them. It almost feels more like a handicap-accessibility issue than a guest list issue, KWIM?
If I had children living at home (of any age, not just little ones), not only would I not expect them to be invited to an unrelated friend's wedding, just because DH and I were, I'd be very surprised if they were, except for very close friendships in which the whole families are close friends. And sometimes only one child is invited, if that one is a friend of the bride or groom. Not offensive at all in my opinion -- whole families do not have to be invited like permanent couples are.
If someone asked if they could bring their children to a wedding that wasn't even their family and then were outraged that other children were there -- "It's not even a child-free wedding!" -- I think they'd be way out of line. If the HC/hosts have children in their lives that they choose to include, that doesn't mean that every single guest be invited with their whole family. It's no more rude to invite some people in family units and others not than to let your best friend bring her boyfriend although you didn't invite every other single guest "plus one."
It amazes me that people seem to think of other people's weddings as quasi-public events all about them -- they feel so entitled to bring dates or children or to have menu choices or their preferred seating or beverages and on and on. It's a very important life cycle event in someone's life (and usually two families' lives), not just a party. It's an honor to be included -- and that includes the reception.