They told us that a reception is no place for children: often they run about and end up preoccupying their parents to the point where the parents miss out on some of the fun. I have never been to a reception where children were not in attendance. What's your opinion on this matter? Also, is there a way to politely discourage guests from bringing their children to the reception?
Whether children belong at a wedding reception depends a lot on the reception and the children. At a casual afternoon reception, held in a setting where not much is breakable, most kids who aren't actually holy terrors will do fine, especially if the couple is easy-going. The more formal the reception, and the later it starts in the evening, the more kids are likely to become a problem.
In my experience, evenings with friends whose kids are under age 7 tend to end before 9 p.m. because the kids are getting too tired to be capable of behaving well -- and conversations with these friends do have a lot of interruptions.
If most of your friends have little ones, and you hope that the party will continue until midnight, there's a lot to be said for not having the little ones at the reception. (Your fiancée’s parents may also be trying to hint that the kids on their side of the family will be licking the icing off the wedding cake before you cut it, and dancing on the tables...).
Ultimately, this one is a judgment call. Think hard about the kids you would invite and your expectations for a successful reception. Large numbers of children do change the flavor of an event. If the timing and mood is right and the kids are pretty well-behaved, this can be good -- children love dancing, and their presence is also an icebreaker for their parents to talk to one another. Little girls, at least, also love brides, so if your fiancée likes urchins hanging from her train, you'll get some great photos (one of our best shows my godmother's five-year-old wearing my veil). But if the event is expected to be quite formal and the dancing and such starts late in the evening, you may be faced with a choral interlude of whining, followed by the early departure of many parents. Or you may know only great kids (some are definitely better behaved than others!) and have no problems at all, even with six-year-olds up until midnight.
One alternative, if you have lots of out-of-town guests who don't have local, uninvited relatives, is to provide a sitter, some videos, and some toys (dollar stores are a good source!) in a separate room at the reception site. In this case, you include the kids on the invitation, then add a line on the reception card that "During the reception, a sitter will be provided for children up to age ##" (with whatever cut-off age you like).
The traditional way to not invite children at all was to omit their names from the invitation envelope -- not all parents get this hint, but you'll discover there are plenty of potential guests who won't get any hints of any sort, so resign yourself to a certain amount of calling people to explain that no, their invitation did not include their stepson, his girlfriend, the other members of his garage band, and his dog Spot. This method, of course, excludes children from both the wedding and the reception, which may not be what you want to achieve.
If you want to include kids at the ceremony but not at the reception, and you don't want to provide a sitter at the reception, let me suggest a method that won't thrill Miss Manners, but that is quiet and straightforward enough to be tasteful. On the ceremony invitation card, include "Children welcome" in the corner copy. On the reception invitation card, put "Adults only" in the equivalent place. The major etiquette gurus would consider this an etiquette misdemeanor, since it's not the "done thing" to point out who is excluded from the invitation -- but it gets the point across quietly, and doesn't draw attention to the problem by dressing it up in fancy language. If you want to be a true etiquette traditionalist and terrify the people around you, omit this corner copy and send an envelope with both ceremony and reception invitations to the parents, then send separate invitations to only the ceremony to the kids (you can use one invitation for all the children in a given household). This tells the well-informed that the parents are invited to both events and the kids to only one... alas, it will probably only confuse most people today, though.
Should you decide to go with the traditional option of separate invitations for the children, here's how you address the cards. A lone daughter is "Miss Amy Smith." Two or more daughters together are "The Misses Smith." A lone son is "Master John Smith." Two or more sons together are "The Masters Smith."