Take into consideration whether or not your event would be a safe and accommodating environment for a child. Maybe this is just simply a venue that is not kid friendly. If this is the case you could of course just ask that children not attend. If you would still like to have them there then make accommodations for them. What would they enjoy while at your event? The perfect idea might be separate tables or a separate room with a responsible sitter. If you choose this option then make sure you hire enough people to take care of and entertain them.
If you are in a situation of having babies in attendance then there is more to consider. Yes, you want the parents to feel welcome. You also want to look back on this day or watch your wedding video without a screaming baby and an uncomfortable set of parents in the audience. If you have a wedding planner, talk to them about the seating arrangements for these guests. They should always be seated near an exit on a row in case they need to leave. Someone on staff for the planner should be nearby to assist them as soon as they need help. This will make for a smoother ceremony and a relieved parent. As far as the reception and babies, be sure Mom or Dad know there is private place for changing and feeding.
Finally, what do you do with an unruly kid? If you have an event planner, send them to handle it. That is why you hire us! If it is just you, designate someone you trust to be kind for that job. Once you have spoken to parents and behavior continues down a bad path, it is perfectly acceptable to ask them to take them out of the room.
The truth is, this is not an easy subject to approach with some parents. Just keep in mind that they are a guest, invited by you. If you make arrangements in advance for these guests, you will be amazed at the difference in the day. The kids and parents will appreciate the thought you put into having them as guests. I have often attended weddings and parties where not only the host is frustrated but also that poor parent of child. When I plan an event I remember those times and am sure to accommodate the kids no matter what the age. It really has made all the difference in the world.