Andor = Pacifists with no ground forces
Thoraxian = Virtually indestructible ground forces
To keep the Thoraxians in check you need to destroy their fleets. To do that, either use your own ships, or get other races to attack them. In your Andor issue, you'll probably need to whittle down some of the Thoraxian ships by yourself, then help the Andors build up their fleet. Even if the Thoraxians love you, they don't really listen to you. More importantly, you don't need them to like you, you just need a way to get them into the Federation (eventually). So pick one of those methods and unless your actions are going to impact that, don't worry about their personal feelings about you. As previously noed, making their planet useless via RCS problems helps some as well.