Now that I think about it, it really doesn't seem like any of the breakaway states are hostile to the Lyrans. Hostile to Trillian Steiner, perhaps, but all of them seem to be dedicated to protecting Lyran worlds that they (correctly) feel the Lyran state has abandoned.
The Timbuktu Collective only exists because the Florida TTM had to fight a rebellion for more than a year unsupported before the Commonwealth deigned to actually protect itself. After they broke away and became the 1st Timbuktu Guards, all they've done is protect Lyran planets from pirate raids (notably, the Commonwealth itself isn't showing up to these fights). Every world they've taken from the Commonwealth has joined voluntarily. If there aren't ideological reasons for defecting (I note that the worlds leaving are places that Democracy Now was strong on, that the Collective is probably just a rebrand of the Rim Collection's government) it's simply because Timbuktu's protecting them and Tharkad isn't.
The Vesper Marches exist purely because the 1st Hesperus Guards showed up to defend Melissa instead of a loyal Lyran unit. Arc-Royal isn't following Trillian's orders, but that's because her orders are "stop liberating Lyran planets and send your leadership to Tharkad so I can make them assume the defensive posture the rest of the Lyran forces are in". The Tamar Pact has an actual secessionist national identity, but they're only interested in conquering ex-Tamar Pact worlds, to the point that they've completely ignored the power vacuum in Skye, which would be an easy expansion route, in favor of fighting Jiyi Chistu's Falcons.
Point being, none of these states seem to be an actual threat to what remains of the Commonwealth for the foreseeable future. The Commonwealth doesn't really lose anything due to their existence, because they've only taken worlds the Commonwealth dedicated no forces to taking or holding anyway. But simply by existing, they increase the Commonwealth's security by providing difficult to digest buffer space. This should allow the Commonwealth to redirect it's forces to repelling the invasion from the Rim Territories, and retaking worlds lost to the Wolf Empire.
tl;dr while the separatists might have been produced by the weakness of the Lyran state, they don't seem to be weakening it. They seem to be improving it's overall strategic position. If Trillian's smart, she'll seek rapprochement with the breakaways. They can always be reconquered after they've served their purpose, after all.