We've just had a reshuffle at work and I've acquired a new team. I've led teams for years but there are a couple of particularly difficult characters in my new team, one of whom I've managed before - the kind where most interactions have to be documented on file and they are never far from any unrest or fall outs at work.
They both perform well in their day to day roles but also undermine and belittle others, spread gossip and are not people you'd want to trust with anything confidential. They are both clever about not leaving a trail - much of this behaviour is conducted in lunch breaks or by text from the toilets so can never be proven and tackled properly. That's the level we're talking. Recently I've had real reason to suspect one of an offence which would usually be considered gross misconduct in most workplaces but my manager wouldn't support me in investigating fully due to the fact that she likes this person's work, I think. (That sounds bloody ridiculous written down but is true 
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We have very busy roles and I really want a happy atmosphere where we all get on with the job in hand. I've managed to rearrange the seating plan so they're seated well apart and one is next to me. Bearing in mind I have limited support from my line manager, how else do I best start off with them to get the results I want?