You will be in the same coalition, I remember playing regularly as the Romulan Star Empire, and all of the Federation worlds show up as specific vassal sectors within the Federation; it is a radically different type of state than just about anything else in the entire Star Trek universe: the Klingon Empire and the Lyran Star Empires are intrinsically feudal and aristocratic, the Romulan Star Empire is itself intrinsically both Imperial and Republican in nature, Cardassia is at core akin to the USSR in world history in an awful lot of ways, including an active secret police (Garak having been a political officer at that for instance!), and the Borg are, basically, a form of a technological missionary religion of sorts; with their emphasis on converting members of other species into themselves, and that simply scratches the surface of it.
The UFP is itself very unusual, so their method of expansion would naturally be unusual; in a sense, it isn't too different from how the Klingon Empire has its own "high houses" that're vassals within the Empire- in several ways they are similar nations in that regard.
The Ferengi kind of have a whole theology based around finances as the core of their society, and it, like the Orions, is intrinsically corporate in nature, same with the Yuridians for instance.
United Earth kind of "evolves" into the Federation capital for lack of a better term, at least according to the mythology of Star Trek. Expect this; though, according to Star Trek canon novels, it was the war with the Romulan Star Empire that was the catalyst for forming the Federation: their attempt at conquest failed spectacularly and the Federation was the result of the attempt by the Rihannsu to conquer Earth.

Jamcarmody, again you miss what he is saying. After you form the federation and join another coalition with say the Bajoran. Then you incorporate the Bajoran into the Federation of Planets, you are left in the coalition with say the Andorian Sector and Tellarite Sectors(which should not occur because they are already in the Federation of Planets with you. This in turn prevents you from joining another coalition with say the Sauran and Benzites if they are already in another Coalition. Also because those 2 nations are in their own Coalition, you do not have the option to ask them to join a coalition with you because they can only be in 1 coalition at a time.

I am having the same issue and can not figure out a work around for it.

For then, it seems as though as well that you've got to wage a war to overwhelm said federation; I've tried many a time as the Romulans, be it in a Federation or not; to annex states that're already inside a Federation. To do so in the only way I know is to wage a war against that alliance and take it over, nation by nation.
I haven't missed the message at all; and this's a long-running obstacle with the Federations within the game.