After you do this. How exactly do you go about maintaining strength as it seems best way is just go to bull and pay $1 for fast at brothel and then I assume you just spam punishment when it shows to, to try lower rebellion orbs? Trying find a faster way to get past the early stages of it as around 6 orbs I'm unsure what to do besides spam punishments
If she is feeling guilty then she's expecting to be punished, and you need to deal with that, but take a pause to consider what you asked her to do. You can choose to give her tasks that she won't/can't refuse. Like sending her to school or hiring tutors or taking her to the arena.
The first two levels of positive mood each raise obedience by one point, and once you get into a "countable" amount of disobedience (which usually happens after 1 point of fear unless she has very high attributes) those points make a difference between F- and D- or better outcomes from school/tutor lessons and whether she will refuse personal lessons or activities at home. Her mood also makes a big difference for lessons when she is more obedient.
If she isn't
refusing what you are having her do, then her obedience isn't the issue, it's her motivation. Mood is very important for motivation, and clothing bonuses also help a lot. If she has a trait that aligns with some activity then doing that will improve her mood and she will perform better, so try different things to see what works. Variety of activities also produces more merit for you to reward, raising her awareness and mood among other benefits.
If you get stuck and her obedience isn't going up quickly, it can be beneficial to allow a slave to become slightly spoiled. They will feel more merit and you can therefore give larger rewards without raising her spoil level above the first tier. Those larger rewards can include taking her on dates which, if successful, will eventually raise her devotion. It's an alternative to reaching positive obedience through fear. More expensive, and potentially slower, but if the slaver is weaker than the slave or there are other factors making it hard to build up her fear then it's a viable approach.