Gaitelreima was the eldest daughter of Guaimar IV of Salerno (murdered
June 1052), and his first wife Purpura. In a charter for Cava abbey
dated January 1087 her three husbands are named as Drogo (of Hauteville,
count & duke of Apulia & Calabria, murdered August 1051), Robert
(probably of Aversa, count of Lucera, died in or after March 1066) and
Alfred (Affredo, count of Sarno, died before September 1081).
According to Amato of Montecassino, a source extant only in an Old
French translation, Guaimar of Salerno married a daughter ("fille") of
the first husband Drogo to Robert of Aversa, count of Lucera. This has
been generally assumed a mistake of the translator, substituting "fille"
for "veuve", so that actually Gaitelgrima's father gave her as the young
widow of Drogo to Robert not long after August 1051.
However, in Francesca Petrizzo's 2018 Leeds University PhD dissertation
linked by Todd in another thread
(
https://etheses.whiterose.ac.uk/21908/1/Petrizzo_F_MedievalStudies_PhD_2018.pdf),
on pp. 104, it is argued that "fille" was correct and that the wife
given by Guaimar to Robert was in fact Drogo's daughter Aumburga (or
Eremberge) who is named by her brother (Gaitelgrima's step-son) Richard
the Seneschal in a charter written after her death dated 1101.
Petrizzo assumed that Aumburga was a half-sister of Richard in order to
account for her having been given in marriage by her purported maternal
grandfather Guaimar. However, she did not address the obvious problems
with this: first, that Guaimar of Salerno would have controlled the
marriage of a Hauteville princess, his supposed granddaughter (who had
powerful paternal uncles including her father's brother and successor
Humphrey Abelard), rather than that of his own young widowed daughter;
and secondly, that Robert of Aversa had only one known wife and his
second son Enrico of Monte Sant'Angelo married a Hauteville first cousin
of Aumburga (Adelasia, daughter of Roger Bosso of Sicily and Judith of
Évreux).
In view of these considerations I don't think the proposal of Petrizzo
can be safely accepted.
Peter Stewart