Well, killing the Thoraxians is the main way, but if you kill all the other races in the protectorate then the thoraxians will be left alone and can be coerced into the federation at that point, too.
In some of the alliance types, like the Solar Axis Pact and Union of Independent States, you can sow dissent between the members and have members break off. With the Thoraxian Protectorate, all of the races in the protectorate have pledged part of their strength to the Thoraxians, and the latter rule through fear. So there's no breaking them off with that particular one. The Thoraxians are getting a 1.2x multiplier to their ship production for each of the other races in the protectorate, while each of those races is at 0.8x instead.
So one of the biggest problems you probably have is that the Thoraxians are being too speedy in making new armadas. If you can slow or disrupt that, then that will create more of an opening for you.
The ground power of the thoraxians is also frankly rather insane, particularly on their home turf. You can bomb them, but the Skylaxians refuse to do that. The peltians are really good at it, but unfortunately they are with the thoraxians in your game. The Burlusts on the other hand are the only race that really can hold a candle to the thoraxians in a ground fight. You could focus on getting their ground power even stronger.
You might find yourself in a war stalemate for a while with the protectorate, in which case directly going for war would just continue the stalemate. A way to get around that would be to try to keep the thoraxians contained while at the same time focusing your main efforts on technology: the main weak spot of the thoraxians. Unfortunately the evucks are also very good at technology, and they are freaking thieves as well. So it might be in your best interest to snuff them out and THEN work on your techs. That way they can't steal techs and then share with everybody else in the protectorate. Killing them would also remove the multiplier they were providing to the thoraxian manufacturing, which is a big plus.
The Skylaxians are by far the best scientific race in the game, and the thoraxians and the peltians are the worst, and the boarines are not great, so you could outpace them within a few decades (handled with super-fast-forward in dispatches for techs, of course -- not just sitting around).
Another way to go, if you aren't going to go for tech supremacy, would be to try and ruin the planets of the thoraxians in various ways. You are very fortunate to have the Acutians on your side, because this is one of their specialties. If you are fed up enough, you can just have them slam a moon into the thoraxian planet and that is that. You have to work on making sure the best industries are in power in order to really get the most out of that, though. You can also dump toxic waste on their planet over and over again, as TotalBiscuit found, heh. That has been nerfed since the time period of his video, though, in the form of other races getting increasingly disillusioned by you if you do that. Which can actually cause the federation to break up, if I recall correctly (check the betrayal percentages in the federation progress screen to see if that changes at all).
Hope that helps!
