if they are going to sitting with their parents, put their name on the place card with their parents, ie...
mr and mrs x
or they could get their own place card. but if you are having set tables, everyone in attendence should have their name on a place card telling them where to go. you don't want the parents thinking little johnny isn't allowed to sit.
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usually parents assume that they are seating with their kids?
It's best that neither you nor your guests assume anything. You plan where the kids will be seated (kids this little probably should be with their parents) and you let people know in the most effective way. Putting their names on placecards with their parents seems to be efficient. If you have individual cards on the tables (sometimes these can indicate meal choices for the waitstaff), then have one for each child as well.
myra at www.classysassyweddings.com