I am sorry you are having to deal with this...but, its not just BRB policy. Most, if not all, "adult only" facilities are this way. BRB charges extra, because like TA Maureen said, your guests would get access to everything there all day. I have been to Breezes Bahamas many times and they stick to this rule as well. Keep your chin up and who knows, maybe another family member who can't make it can watch your cousins kids so she can have some "Adult" time to relax and enjoy herself.
And about your family members not coming...you are not the only one with this. My mom was the most important person I wanted there...and she will be there! Everyone else is a bonus:) Most of our guests are our close friends which I am thrilled they are able to make it.
I am also getting married at BRB so I can help you out with anything if you need..there aren't many BRB on here so we gotta help each other out!
Good luck:)