Dear Christine, 

Your question is simple and it boils down to this: do I have to have 'full disclosure' with the spiritual director who is helping me discern my vocation?  

First, though, let us consider the problem you had. It seems you have put it behind you, having confessed it, made up your mind to change your habits, and followed through. So on the surface it would not seem to be an out-and-out impediment to religious life. Nevertheless, it did indeed take place, and it tells you something about yourself. 

You will have to mention it at some stage (not all the details, but just as much as you have said here) at least to the person who is ultimately going to be responsible for accepting you into the religious order you want to join. You can understand why. It is part of the whole picture of yourself, and that person needs to know it in order to give you reasoned and sound advice as regards entering that vocation or not.  

As regards telling the spiritual director you have now, while it is not absolutely necessary, he will probably be able to help you more if you do. He will be better able to tell you if it has a bearing on your vocation, he will put it together with everything else he knows about you, and will prudently examine if it changes anything as regards your having a vocation.  

As regards your father's reputation, I do not think it is necessary to mention him as you explain what happened. It would be enough to say that you found these sites book-marked on the computer without saying who did it. However, even if you did mention it was him, neither your spiritual director nor the person who interviews you for the order will speak to anyone else about the incident, so it will not go beyond them, and your father's reputation would not be affected.