This definitely violates housing codes; limit is typically 2/room, disregarding children under 6, 12, or 24 months, depending on state. Also, children sharing a room usually have to be same-sex.
Of course, if it's their trailer, they aren't going to get into trouble. You usually only run into this problem in "nosy neighbor" or landlord-tenant situations, which this obviously isn't.
So, yes, it violates housing codes, but they can choose to live however they want on their own property. If someone gets curious and calls CPS about the overcrowding, there may be an issue, but that is the only thing I can comprehend might happen.