MedLands allows a different construction:
WALTER FitzAlan, son of ALAN FitzWalter High Steward of Scotland & his wife --- (-1241). He succeeded his father as High Steward of Scotland. "Walterus filii Alani domini regis Scotie senescallus" donated property to Paisley monastery by undated charter[1198]. The seal of "Walteri filii Alani" is appended to a charter under which "Walter son of Alan the Stuart" confirmed the donation of land at Edmonstone to Melrose by "Walter the son of Alan his grandfather"[1199]. Alexander II King of Scotland confirmed the donation of land "in Tibermur" made by "Walterus filius Alani", in confirmation of a donation by "Suanus filius Thori avus eiusdem Walteri", by undated charter[1200]. "Walterus filius Alani" confirmed the donation of "Tubermure" made to Scone abbey by "Swan filius Thory auus meus" by undated charter, dated to before 1221, witnessed by "Gilbto comite de Stathern dño Robto filio ei, Rogero de Mortimer, Galfrido de Inutunglas vic de Pth, Dunecano fil Moregrund, Reginaldo de Warenn, Walto filio Swani, Henr fil Alani fil Wani…"[1201]. He adopted the name Stewart. https://fmg.ac/Projects/MedLands/SCOTLAND.htm#WalterFitzAlandied1177B
The deal here is that this Walter is the grandson of Walter fitz Alan by his older son Alan fitz Walter, who was probably *not* the son of Eschina de Molle. We don't know who Alan fitz Walter's wife was either.
The literal meaning of "avus" is "grandfather", but it was also used more loosely to mean simply "ancestor". If taken literally, it would mean that Alan fitz Walter's wife was a daughter of Swan fitz Thori; less literally, the reference may be to (grandfather) Walter fitz Alan's unknown first wife. Either way, it's a distaff side connection and can hardly be interpreted as anything else.
There is no primary evidence for the existence of an "Emma, daughter of Walter fitz Alan".