I am a mom that has raised three boys and have had friends that have been in your position.
If this just started...It's NOT a mood disorder. Counseling can help. But what I am reading between the lines here is that you work a lot, your daughters natural father may or may not be in the picture. Whatever this is, it plays a factor. Your length of time with the new boyfriend plays a factor. How involved he is and how he reacts to her, plays a factor.
She is in early puberty, this plays a factor. What she is doing is SCREAMING for attention. If she does not get the attention she needs right now and it has to be constructive, this will only worsen.
She needs to know that no matter what is going on in her life that you are there for her. There has to be time set aside for her and I know this is hard to do raising three and working and trying to have a relationship for yourself. But above all she is the important one here. A reward of good behavior could be just you and her going window shopping, playing a board game that is at her level. She needs that girl time and she needs her mom right now.
The choices she makes are dependent on the choices you make for her. You can not change a childs world and expect them to just accept it. She will eventually influence the younger children in the household. She will eventually reach out for attention in the wrong places.
She is the oldest. I was the oldest with out my father. It's an abandonment issue as well.
You also have to be firm and consistent with it. Consequences are consequences and rewards are rewards. And lots of love has to be put into it. Do not give a huge amount of attention when possible to the bad behavior. Make it quick and firm. Then make the time to talk. Find what interests her and utilize that to find ways to talk to her while she is distracted. Also Give her some power in her own life. Let her pick something to have a say so over. Your job as a mom of a future woman is to empower her with pride, self fullfilment, AND self love.
If you do not have it for yourself she is going to read right through it. Allow her to let those real feelings out when it is apropriate. Make that time happen for her, discuss the frustration she is feeling. Let her tell you like it is with out taking it personally.
Then say OK...From now on we will do this every...so and so time at this place and you will not show the behavior at school or work. This is direspectful... And what can I do to show you more respect. You will see a real difference in how she handles things.
Let me know how it works out,