Yes, Mabel was a half sister, but they did not share mothers - they shared fathers. They were both McGregor's. My grandfather (who was named for Archie Payne) knew all of the siblings well and remembers them fondly, including Mabel. He never mentioned a sibling named Alex and said that Archie was the oldest. Where did you find the info on Alex? Maybe you should email me? email@example.com
I think I have a LOT of info on Archie, Mabel, and their parents/siblings that might help you.