I have re-read the full entry for Alexios in the genealogy by Barzos,
and I'm not much the wiser for it.
He did cite the Russian sources for the marriage in 1122, but then
disregarded the implication of this when discussing the puzzle of
Gautier's source for placing the first wife's death on 16 November 1131.
Unfortunately this source is less than satisfactory - it is found in two
contradictory marginal notes in a copy (or perhaps in two different
copies) of the rule of St Pachomios. Barzos cited a compilation made in
1928 but unpublished. The first note implies that the wife of Alexios
died on 16 November 1131, calling her Eudokia, and the second calls her
Eirene. Barzos assumed that the name Eudokia in the first indicates that
she was the Kievan princess whose original name he accepted as Dobrodeja
(equivalent to Eupraxia, though as I wrote before this is probably an
invention from the 18th century).
Barzos tried to determine more exact information about the source, which
had come his way with no substantiating details, but received no reply
to his enquiry.
He was confident that the Kievan princess had not yet married Alexios at
the time of his coronation as emperor in 1122, and that she was sent to
Constantinople to be married, and crowned herself, shortly afterwards.
This fits with a Russian source placing her departure in 1123, and
another saying that she was sent to the emperor "in Greece" - which by
this chronology could have meant to Alexios rather than necessarily to
his father Ioannes II as it has been interpreted.
A better and fuller discussion of this marriage can be found now in
Dariusz Dąbrowski's *Genealogia Mścisławowiczów: pierwsze pokolenia (do
początku XIV wieku)* (Cracow, 2008).
The second marriage, to the Georgian princess named Kata, was accepted
by Barzos, placing her as a daughter of King Demetrios I. This was
mentioned in Rafał Prinke's article (p 496 note 35: "Confusion between
the two Katae arose because a scholium to the Chiliades of Ioannes
Tzetzès identified the Kata mentioned in the Chiliades (line 596) as the
wife of "porphyrogennetos Alexios" (i.e. son of Ioannes II). Some
historians, thinking that "our" Kata was meant, assumed it was a mistake
because Alexios had another wife at the time (Dobrodieia-Eupraxia of
Kiev). See: Paul Gautier, "La curieuse ascendance de Jean Tzetzès."
Revue des études byzantines 28 (1970): 208-209, footnote 5. Gautier was
himself confused but suggested Kata may have been the second wife of
Alexios, which Vannier later confirmed and, following Barzos, identified
her as a daughter of Demetrios I.")