We have a bit of info as to what the Taurians were up to:
1) Though the Cappies have been historic enemies of the Concordat (at least 2 wars in the Age of War IIRC), the Fed Suns ended up taking the vast majority of their territory during the Reunification War. As such, the FedSuns have ultimately (with the help of the SLDF) done more damage to Taurian Pride than the Cappies have.
2) The Taurians (with the exception of their brief war against the Canopians over the New Colony Region) seemed to focus on rebuilding themselves after the fall of the Star League. Everyone was doing badly, and the Taurians decided to reinvest their efforts into rebuilding and defending what they had left rather than burn forces in the Succession Wars.
3) The Taurians have, historically, been isolationist and not particularly imperialistic. Again, aside from the Concordat-Magistracy War I don't believe they have ever fought a war of conquest, and all their previous expansion has been through peaceful colonization and accepting worlds into their nation. As such, getting involved with the Succession Wars would go against their fundamental mindset. The one time they tried this trick, it turned out poorly (see war against Magistracy).
4) During the 3025-3050 era, the Concordat did a LOT of colonizing, and that takes up a LOT of resources that they weren't putting towards their military for expansion. Thomas was building up defenses because of his increased paranoia (made worse by the ravishing his family took), and the Far Lookers took MASSIVE funding to found all those colonies which showed up. This is at least part of what kept the Taurians subdued during that era, and one of the impetuses for Jeffrey taking over as I recall.
5) The Taurians were always more willing to accept a Capellan alliance over a FedSuns one, for as I mentioned above despite the Capellans raiding and going to war with the Taurians, they have historically done less damage (or, at least, were less visible in their imperialism) than the FedSuns. As to an alliance with St. Ives, I don't recall that treaty but I could see issues with that. For one, the Compact was allies with the FedSuns, who are the "Big Bad Imperialists" in the Taurian collective psyche. For two, St. Ives is far away and the Capellans are right on the border. What can a half-dozen worlds with a smaller miltiary (on paper) than the Taurians do? What does the alliance do for them?
6) After Jeffrey's death and Grover took over, he was a proponent of the anti-FS faction (Jeffrey was far more moderate in this). The Cappies made an alliance with the Concordat's historical allies in Canopus, and their express aim was anti-FS. Since the Capellans had a better reputation than the FS did, of course Grover took the chance. The Capellans were on the rise at the time, having bloodied the Suns in retaking most of the Sarna March.
7) While on paper the Capellans left the Taurians high and dry, taking more from them than giving back, the Taurians still came out with a pretty big industrial boost as part of their alliance which is probably why the Taurians didn't withdraw when it became apparent to them that the Canopians were getting a better deal than them. Until the whole Fighting Urukhai incident, the Taurians weren't actively threatened, so they could afford a less-great deal as long as they were still getting some good stuff out of it. After the attack on Taurus (the world that had never fallen, remember) the people of Taurus were inflamed by the breach of their soverignty, made worse by Grover's rhetoric stirring up FS hatred. Combined with the Word of Blake talking Sweet Poison in their ear, the Concordat was gearing to start a war they couldn't win.
8) When the Jihad hit and the Taurians were able to actually take and (for a while) hold territory from the Suns, they started to believe their own hype about taking the war to the Suns and thinking they could win. Only, when the Suns stabilized and could deal with the Taurians attacking them in the boonies, they were able to CRUSH the periphery riffraff. The level of crushing defeat led to the current TC troubles.
Anyway, a few thoughts on the matter.