There are times when being fair is unfair.
Yes you are obviously having a great laugh with her, but she isn't as hard working and diligent as your other assistant manager and her team. The latter being the reason why the assessment was passed so well.
You also shouldn't check up gossip about your assistant behind her back as it just undermines their position.
OK you are a little green and unused to a position of responsibility, mistakes will be made while you adjust. But you have to realise that what you see as fair demoralises your good staff who see others getting away with murder. It doesn't have to be a screaming bollocking just a little reminder. And praise your good people at he very least.
You have to remember that the pay and incentives isn't the best around and they know that. You can also try replacing them when they go, even in this market it'll be very hard.
Oh, and to be very blunt what you think makes you look cool and Branson like just reminds people of David Brent.