I think it was the Doukas family that was (undeservedly) powerful at the time of Alexios's ascension. Eirene herself was 15 years old, Alexios was 25 and Maria of Alania was 28, and she had already had one son by Michael VII - Constantine.
I think, in OTL, before John II was born, Anna Komnene was betrothed to Constantine originally, but then he died and she was married to Nikephoros Bryennios te Younger.
Sorry, I'm just really biased towards the Doukas family. Constantine X did away with Isaac I's reforms and disbanded the army at the worst possible time, and none of his sons (Michael VII, Andronikos and Constantius) had any experience or interest in ruling.