This is something you should double check. The exception comes directly from the database and not from Entity Framework. It's likely that also a table structure with the same constraints created by hand will be invalid.
Keep in mind that your foreign key properties Mother. FamilyID Father. FamilyID Child.
MotherID and Child. FatherID are not nullable so they represent required relationships and the corresponding columns in the database are also not nullable.
This is a known problem and you're not the first to bump into it. From what I've heard they are working on a better solution in the upcoming version of WCF, however for the time being from my experience you are much better off creating DataContracts that represent the data to be sent over the wire thereby changing the data structure to remove the cyclic reference.
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