I think Tamar and the Commonwealth come up with some kind of arrangement that lets both of them save face. It'll be worded in such a way that Tharkad can say Tamar is still Lyran, and Tamar can say Tharkad has recognized their government. They'll keep using the same money, rank structure and such to present the appearance of unity to outside nations. But I don't think anyone else gets a sweet deal like that except maybe the AML.
The writers aren't even pretending Arc-Royal is a separate state, so I'm not going to either. One way or another the beef will get squashed and Callandre becomes Margrave of Arc-Royal, going from Mid Career Morgan Kell where she is now (running an autonomous region of Lyran space denoted by being a slightly different color) to Late Career Morgan Kell (important political figure within the system).
The Vesper Marches are going to make like Neo-Tokyo and *E*X*P*L*O*D*E* once those worlds that thought they were rejoining the LC find out that they didn't. One of them is Gareth Dinesen's world, just to add a little more spice to that mix.
The AML, though, they're going to be more than capable of working out a pleasant status quo with the Lyrans, given that the alternative is the Horses, who are gonna take one look at their Chalcas asses and try to put a boot up them.