Question: Probability Christmas names in a hat ...coincidence?

So, every year our family picks names for Christmas, but this year seemed odd.  My wife pointed out that one family always just happens to randomly pick another families name.  That is the majority of the time most of one family is always trading with another, the only rule is that each family member can not trade with a member of their own family. 

I was wondering if someone could come up with a way to calculate just how random the choice actually was from the previous year or years using whatever means necessary .. graph theory came to mind.  The draw was done behind closed doors, so my wife questioned how failrly that was done, and so brought me here with the question ...
Was the name choosing really random or was it actually a fixed draw?

In our group there are total of 9 adults and 9 children, but actually the 2 youngest children swap gifts so it's really 9 adults and 7 children who can swap presents.  But I will breakdown the families less the two trading children.

Family A - 2 adults 1 child
Family B - 2 adults 2 children
Family C - 2 adults 2 children
Family D - 2 adults 2 children
Family E - 1 adult

Oh, a child can trade with another child or a parent and similarily a parent can trade with another parent or a child.  

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