Who was Redburga?

Redburga or Raedburgh, wife of Ecgbert, King of Wessex, and was said to be "regis Francorum sororia" which translates as "sister of the Frankish King". This can be only in reference to Charlemagne; however, no such sister exists. My arguement is that Redburga was actually Charlemagne's sister-in-law and was sister of one of his wives, possibly his fourth wife, Luitgarde. As follows: Charlemagne or Charles the Great, was King of the Franks and Emperor of the Holy Roman Empire. He had only three documented siblings: Carloman, his elder brother; Pepin, another brother who died young; and his beloved sister Gisela. However, Gisela was consecrated to a nunnery since girlhood, and so could not be the Redburga above. However, Charlemagne had four wives, and it is his last wife, Luitgarde, who I believe is Redburga's sister. King Ecgbert of Wessex was an exile at Charlemagne's court at the time he and Redburga wed, circa the year 800 -- also the year Queen Luitgarde died. Ecgbert must have met his wife at Charlemagne's court, and the sister of the Frankish Queen would not have been a bad match considering. In the year 802 Ecgbert returned to Wessex, ruling peacefully as King. Circa the year 805, their son AEthelwulf was born, and after that Redburga disappeares. Besides the helpful chronology, there is also the part of the phrase "regis Francorum sororia". Used as an adjective, "sororia" translates as "sister", but here it is used as a noun -- thusly translating as "wife's sister" or "brother's wife". Thusly, I conclude that Redburga was indeed the sister-in-law of that most famous of Frankish Kings, and possible sister of Luitgarde. Written by Jessica Key. Sources: "Pedigrees and Progress" by Wagner, "Britain's Royal Families" by Weir, "Plantagenet Ancestry of King Edward III" by Moriarty, "Ancestral roots..." by Weis, and Re:Redburgh/Raedburh: meaning of "sororia" by Jean Claude Chuat.