Obviously, as the planet from which Golion hails, Altea would be one of the first members of the Alliance. Princess Fala (Allura) was chosen to be the Alliance's representative for Altea (rather than Raible whom was both military strategist and steward and would have been a better choice) because she was the pilot of Blue Lion and brought with her the image of strength and power. However, it is interesting to note that in the very next episode the rest of the Alliance calls her "strength and power" into question because she pilots Golion's leg rather than his head.
In an earlier episode of the Golion series the planet Earth was destroyed. Completely. Totally. Nothing left of it but space dust. One must wonder then why they even bothered including it in the Alliance seeing as how there are only a grand total of five Earthlings left in the galaxy (Kogane, Kurogane, Seido, Shorty and Ryou). The representative of "Earth" is Kogane because, for all intents and purposes, he is the sole leader of Earth's people (all five of them).
The planet from which the "Amazonia Flowers" are from. It had been held under Galran control for countless generations, the people being forced to grow and harvest the planets mystical flowers for their life giving properties in order to extend Emperor Daibazaal's already long life. They were freed, not by Golion, but by Kurogane all by his loansome. The representative of Amazone is Mister Duran.
A desert planet that greatly resembles the bastard child of Mos Eisley, Tatooine from Star Wars and Persia circa the 1400s. They are freed by Golion in season two. The representative of Jarra is Commander Bohan.
Altea's sister planet, when Heracles was first introduced it was one of the villains. There had been a rivalry between the two planets stretching back to the founding of the Royal House of Altea and the King of Heracles asked Daibazaal for aid in settling the old fued. The Galra Emperor was more than happy to oblige him, turning the King's eldest son, Samson, into a Death-black Beastman. Sincline later blows the treaty by firing on and killing Samson while he's fighting Golion. Heracles then realizes that they were wrong to trust Galra and they join Golion in their fight against the Empire.
It should also be noted that Heracles is the only planet in the Alliance that actually have a space fleet. Even Altea which has Golion does not have any other space-craft designed for war (with the exception of castle Gradam). As such, Heracles is probably the only actually useful member of this whole little Alliance. The representative of Heracles is Prince Alor.
Yes, that's actually it name "Sand Planet", the writers never gave it a real name. As its totally unique and creative name would suggest, Sand Planet is a planet covered entirely in sand! Ooh... aah... And is populated by the Sand People (please, contain your astonishment) which greatly resemble pokemon. Sincline attacked Sand Planet in season two in order to try and capture some of the natives to turn into Death-Black Beastmen and he manages to conveniently capture the only one that was befriended by Princess Fala. The representative of Sand Planet is Doctor Harvard.
It should also be noted that while Sand Planet is populated entirely by Sand People whom are not human, their representative in the Alliance is a human. This brings up a whole mess of questions about inter-species racism, don't ya think?
The seventh and final planet in the Leo Alliance, Mura was the planet on which Sincline celebrated his 109th birthday. During the party, the planet was attack by Golion for no morally justifiable reason and "liberated from Galran control". Why they would want to join the Leo Alliance after having their planet assaulted by our "heroes" one can only guess. The representative of Mura is Commander Mac.