I would guess that it's fairly likely that you may develop some sort of thyroid dysfunction if so many close relatives have experienced it. My mum has hypothyroidism and I have so many of the same symptoms as her (usually cold, tired, etc) but not to the same extent as she has them when she's not taking her thyroxine.
I'm assuming that some day in the future it may develop into something a bit more serious but at the moment I'm perfectly fine (if a little chilly..). I wouldn't stress about it now. Obviously keep an eye out for any possibly symptoms etc and see your doctor if anything unusual is happening but I really wouldn't worry about it now.
It could just be that you have inherited a predisposition to the disorder, but that it may never fully develop as it has with your family. As your mum is only borderline this could easily be the case.