Are we allowed to bring our kids to the nude beach, or is it for 18 and older only?

I would say it depends on the country and on the type of beach. There are beaches in France where I live which are known to be for homosexuals dating and other parts where exhibitionists do their things and even have sex in public. But only a short distance from there families will be and everything will be clean of anything sexual. In general resorts or private nudist beaches are very family-friendly and a lot of families go there with their kids. I would recommend checking first what kind of beach you're heading to. (Anyway here in France the government forbids the access to any beach so we're prisoners in our own home.)