You will not be held responsible for your Father & Brothers' nefarious actions unless they involve espionage, terrorism (in all it's guises- including severe & inflamatory neigbour disputes) or political extremist activities.
As long as you have not been implicated, involved, nor prosecuted, then you cannot be held responsible for those in your family who choose to lead a life of lawlessness.
If it's simply a case of you have been involved in any illegal activities but not yet prosecuted, then the RN/RM is not for you. If, however, you have remained uninvolved, then you are not implicated and cannot be rejected by association alone.
Thanks for the info, i myself have never been in trouble with the law, the reason for me asking is i have been informed in the interveiw stage they ask about family life,im not gonna lie to them but mine hasn't been very peachy but wouldn't want that to effect anything during checks.
Believe me, you are far from alone coming from family backgrounds similar to your own. I've lost count of the amount of potential joiners, who, for example, have mothers & fathers who are alcohol or drug dependent & have had a pretty awful upbringing yet remain remarkably unaffected.
Just be honest & look upon the job as a chance to escape from the word in which you live, with complete equality & as many life-enhancing opportunities available as you have the willpower to take.