What our family has done more than once is to hire a student that we know personally, or a regular babysitter of the in-town kids, to watch the young kids during whatever part of whatever events in which they aren't included. People seem to feel more comfortable with someone we knew and trust than a complete stranger, no matter how professional or well vetted.
This might mean in a playroom elsewhere in the venue where the wedding is taking place, at the home of the local cousins or friends whose kids are also not included, or, if the wedding reception is in the hotel where the guests are staying, in one or more of the families' rooms -- that works REALLY well -- that way even if the kids are invited, they can go upstairs and have a pajama party with the sitter, with Mom and Dad just downstairs, and the parents don't have to leave. Sometimes the kids even prefer that, and pizza and soda for all of them and for the sitter costs less than just one reception meal. I wouldn't put it to a referendum, but if there aren't too many families, you can even ask them what they and their kids would prefer.
As our family is spread out, weddings always take the whole weekend, and even when small children aren't invited to the ceremony and/or reception itself, their parents often bring them anyway, and then they are included in the other events of the weekend. So no one has to find child care for an entire weekend even if kids aren't invited to the wedding itself or just the ceremony or something.