Your problem seems to be that you are over-worked. 14 hours of work per day is much too long. So, as you observe yourself, you are tired and irritable when you come home. Since you are perceptive and can put your finger on the problem, the solution will also have to come from you. Here are a few tips which could help.
Do not use the word step-mother, or even more importantly, do not think the word. We have all been brought up on Cinderella and tend to think in stereotypes. I find that even TV news readers use terms like step-motherly treatment and I am always upset at the lack of sensitivity on their part. Even if you had been the child's biological mother, you would be getting irritated because of your state of fatigue and frustration. Perhaps you are trying too hard to supervise and monitor your daughter. And when you are tense, every minor situation tends to get enlarged. I think that a certain level of judicious neglect is welcomed by all children. We do not have to know every detail of a child's day or make sure every handkerchief is smoothly ironed!
Instead of being a dutiful mother, try to be a friendly and playful one. Do not start disciplining your daughter as soon as you walk in. Think of something interesting or witty to say. Give her a surprise present (not every day). Give her small responsibilities in the kitchen and be sure to mention it if she has helped with the salad or some other dish. She should find you fun to be with and will then willingly include you in her activities. Some people want to be perfect in everything they do and this becomes a problem. Just plan to be good at what you do, not perfect. Maybe you should downsize your job or increase your domestic staff. All the best in your relationship with your daughter.