Willy,
A replacement trigger may or may not solve your problem.
The problem you describe is caused by mis-fitting of the trigger and cylinder locking bolt, or the trigger and the double-action fly. If the locking bolt releases the cylinder before the double-action fly engages, the cylinder will rotate before the hammer starts to cock.
If the double-action fly fails to engage before the locking bolt releases, you get the same thing. All S&W actions have the potential for this happening, but a strong trigger spring reduces the chance that the trigger action will hesitate and allow the event.
I would diassemble and clean the triggger rebound spring housing first, and look for burrs, metal chips, or dirt that may cause the trigger to hesitate. If the trigger spring is weak or too compressed, replace it
HTH
John.