My opinion is a lesson that I recently learned............YOU CAN'T TAKE OTHERS PEOPLE"S behavior / talk/ attitudes personally. I use to, and I got hurt alot.......it is hard for me to remind myself to not take it personally. People are complicated. and not everyone is able to say exactly what they intend or mean. Everyone has a different nature about them, and you just have to let people act in their nature.
So try not to care so much about everyone else, yes care about you! You deserve it.
If you happen to have an asst. manager that likes to lie, exagerate, so what.....it's her nature, and tommorrow it'll be something else. Just be true to yourself, live by example, and I think the others are acting like babies. People are allowed to talk. And if the other stylists have clients that are more interested in you, and want an appointment with you that is their right and a good sign that the previous stylist didn't satisfy the customer. If they did, the client would be loyal.
I think your actions of talking .........(answering a clients question) was professional. I think you confronting issues with your coworkers was professional. I also think telling everyone to busy working and quit their gossiping is also professional.
That is just my opinion.......thanks for reading.
Good Luck with them,