Alarm bells are going off in my head!

First of all, you are the only non-family member in the office.  This can be a very bad situation to be in.  If all of the family members stick together, you are the fall guy.  If they don't stick together, you are the one they run to to complain about each other.  Either way it is a very sticky situation.

Secondly, you say that the boss wants you to do collections but he feels you will "piss off his customers" and that he doesn't fully trust you.  It doesn't make sense that he would say that about you and yet want you to handle collections.  Collections should be handled by someone who is trusted enough to be able to represent the company.  I would proceed very carefully here.  If he already feels this way about you, the first time a customer complains about you (and they will just because you are trying to collect money from them!), he is more likely to believe their side of the story than yours.  It doesn't sound to me like you will have any backing at all.

I agree that bookkeeping should be done in a quiet location if at all possible.  However, in my opinion, the physical environment is the least of your problems.  Please think carefully whether or not you want to continue working for this company.