In all things, there's one thing to remember: you are the Moderator, essentially the police officer of your Group. If you are the Group Owner, you have the final say in all matters pertaining to the Group.
I have found that the best thing to do (for me, anyway) is to post a monthly message, at the beginning of the month, which contains the Group's rules and posting guidelines. After that, Members will KNOW what the rules are and what's expected of them, and what could happen if a Member violates the Forum Rules.
If you have more than one Moderator, one thing you could do is delegate specific responsibilities/tasks to specific Moderators, so that you, as Group Owner, don't have to do everything yourself (you still have, as Group Owner, the final say in all matters if a conflict arises). The Members of my Group generally behave and police themselves, so there is often little for me to do.
Remember, it is your Group, you have the final say about "what goes" within your Group. And always remember to put your pride into your pocket when dealing with miscreants, to ensure emotions/feelings do not get in the way of your duty.
-- Paul Gray.
“Time, hurries swiftly on,
Each fleeting year seems shorter than the last,
And many hopes which cheered its opening dawn,
Are buried with the past.”
~~ Mary Ann H. Dodd Shutts (1813–1878), "Passing Time"