The exact identity of Erzsébet of the Kumans, Queen consort of Hungary's parents is not known. Primary sources mention that she is the daughter of the ruler of the Cumans. For example from Elizabeth's seal on a 1273 cirtificate, which reads "ELISABET DEI GRATIA REGINA VNGARIE ET FILIA IMPERATORIS CVMANORVM." http://mek.niif.hu/00800/00893/html/img/nagy/1e81.jpg
But, the question is which Cuman ruler is she the daughter of? There are multiple candidates. Following the devastation of the Mongol invasions, the Hungarian king Bela IV allowed the Cuman refugees to settle in Hungary in 1239. As part of this treaty, Bela's son, the future king Stephen V, married a Cuman princess, who took the Christian name Elizabeth. Some historians assume that she is the daughter of Köten/Kötöny, who was a leader of the Cumans who settled in Hungary and who was murdered by distrustful Hungarian nobles. Another candidate for her father is the Cuman ruler Szájan (Zeyhan), whom Bela IV mentions as a relative in a 1255 certificate: "Zeyhanus karissimus cognatus noster, dux cumanorum... dictie cognati nostri ducis Zeyhani" Source: Nagy Imre: Hazai okmánytár. Codex diplomaticus patrius VIII, page 62. https://library.hungaricana.hu/en/view/KozMagyOkmanytarak_HazaiOkma...
Another option is the Cuman chief Alpra, who the leader of the Cumans in Hungary during the 1260s and 1280s. See Kun Erzsébet Nőestvére (Elizabeth the Cumans' Sister) in Turul (1922-23 editon). https://www.arcanum.com/en/online-kiadvanyok/Turul-turul-1883-1950-...
On many places on the internet, I see it written that Köten II, Khan of the Kumans 's son-in-law was the Kievan Rus prince Mstislav "the Daring" So I think the Russian princess mother (daughter of Mstislav the Brave on Geni) for Elizabeth is just a mistake. I am still trying to track down a proper source for Mstislav's and Koten's relationship though.
On a side note, the entirety of Köten's ancestry here on Geni looks like it is all nonsense to me. Is there any chance that the users who manage the profiles for Suthoi, Khan of the Kumans and Kotian Сутоевич, Khan of the Kumans could provide some primary source-based evidence for their existence and their relationships? I am not finding anything. Geneanet.org does not count as a quality source.