Note: I'm not a doctor or a medical geneticist.

You can research this condition for free on PubMed, www.pubmed.gov.
It's an autoimmune condition related to lupus, and like many autoimmune
diseases, it's believed to be triggered by an infection -- the body makes
antibodies against the infection that happen to also react to some normal
body constituent, in this case phospholipids.

Hughes Syndrome is not listed in OMIM, a database of all known hereditary
dysfunctions, but there is usually a familial tendency in autoimmune
diseases, simply because if your immune system made this particular
error, it's more likely that immune systems of people related to you
will tend to make the same error than in the population in general.
Since you have the condition, should your children show symptoms at any
time in the future, HS should be higher on the list to test for than it
would be for other people.  You should talk to your doctor and/or your
children's doctor about this.

The familial component in autoimmune diseases is present but generally
not very large, so you shouldn't worry too much.  Unless I'm missing
something, 'carrier' is a strange and inappropriate term here.

It appears that Hughes Syndrome is a hot area of research, as it becomes
clear that it's more common than was thought.  It has a wide and varying
array of symptoms, so many people who were known to have some kind of
mysterious probably-autoimmune disease can now be shown to have this
condition by lab tests.  It looks like there are some promising treatment
strategies developing.

Best wishes to you and your family.