Cool, the most positive thing here is you notice your anger, this means you are already more aware than a lot of 9s who shove it down.
Unfortunately, there is no magic solution, the answer can sound simple, but it's is super uncomfortable to work through the anger, especially when you're in a space where the rage is prominent and in the front of your mind. My own experience started from a step behind you where I didn't even recognise the anger, it then took a good 18 months of feeling like I was permanently raging to work through it and become assertive about my needs, on the other side of that though; I now LOVE my anger, it is boundaries and an early barometer that something is not okay.
Look at how 8s use their anger, well, the ones who are effective with it not the ones people are scared of and secretly think are asshats; it is one of their first responses to a situation they're not happy with, they are in control of it, they are blunt, direct and forceful, they shut shit down before it goes too far, they do it without pretense or emotionality. If there's a problem; fix it, move on. The average 9 is the opposite, anger is the last resort so by the time it's surfaced it's like a splatter gun, no one really knows what the problem is cause it seems to come from nowhere, is frequently misdirected then disappears without resolution. As a 9w8 you have it within you to use your anger like an 8 does, while keeping the positives of the core 9 in place, and the key to that; they use it early.
You need to take control of the anger, use it as motivation, it's your grit and determination and constant reminder that your needs matter, it can be a positive force for you.
IME, the only way to do that is to allow it in, sit with it and feel entitled to it, recognise why feeling slighted matters so much, what is the internal message you're getting when you feel mocked and why is that so hurtful (I'd suggest it comes back to that E-9 issue with feeling dismissed/unimportant/unwanted). Embrace the rage while reviewing what's happening internally then experiment with different approaches. Initially it will be hulk rage but through observation and practice you can start to control it. If you're not looking at what's happening internally then change will be hard. Don't be fooled into focusing externally and thinking this is about other people, it's about you and only you. No one else gives a shit if you're angry or not so other people do not matter here, it's what's triggered in you and how you own that. How often to you let people mistreat you, how often do you dismiss your own needs, these are the things that build up rage. How quickly after the rage you dismiss your right to have felt it is what continues the unhealthy cycle where you feel out of control.
If you notice yourself questioning your right to feel anger, or feeling bad/guilty about having been angry; stop, sit with it, remind yourself that you are entitled to it.