From this issue it sounds like the DoL are an old team, perhaps linked to the historical daughters of liberty. 60/70s comics show the Carters as a wealthy Virginia family, so it makes some sense for some to be linked to such a group.
That version of Peggy originated from some android game. The premise of the the series allowed it and stuff like Tessa Thompson-Valkyrie and western T'Çhalla.
This on the other hand looks like retconning of Peggy and of Sharon's history,and it is happening in a long running series. Either someone who really likes Peggy got put in charge in the last year and a half or... That's the only possibility that makes sense.