Which organization's rule set are you using? Please provide the rule number, if possible.Technically if your umpire knows the rules and the pitcher had the ball in the circle and did not make any attempt on the runner as soon as she heads back to first she is out!
Most umpires now wait for the opposing team to know the rule and ask for a ruling before calling the runner out but there are still some umps that call it immediately because they know the rule and enforce it.
Long story short when a player gets walked and wants to take second because you have a runner on third they better not break stride to second without the pitcher making a motion that she is going to make a play on her.
So the original poster, in your scenario the umpire knew the rule and was correct in calling the runner out if they deemed she circled the bag towards second and the pitcher never made an attempt on her. Once rounding first she is not allowed to return to first without an attempt from the pitcher. (This only pertains to a walk scenario.)
I ask because in most, if not all, of the major rule sets discussed on these forums, the batter-runner is allowed to stop once between the bases, and either immediately continue on to the next base or immediately return to 1B. What it sounds like is that an umpire misapplied the rule in a game 3 years ago and you've accepted his/her misapplication of the rule. What you are teaching your players is the safe approach. Your players should never get called out for LBR if they follow your instructions. But you are limiting your team and possibly giving your opposition an advantage.
For the record, I umpire mainly under USA/ASA rules. I don't have a rule book handy, but I can tell you that the LBR is covered extensively in the main body of the rule book, the Rules Supplement section, and in every rules and mechanics clinic I've attended over the years.