That really could've happened in a multitude of ways...the monotheistic power structure seemed to be very tumultuous and prone to violent shifts - It seems just as likely that someone made a move to remove the Mother and Lacy took advantage of the situation with her little army.

As for Daniel controlling the robots, I just linked it to the program he had the doctor steal - it's not like he just plugged in his laptop to some coffee shop wifi and started typing in orders. There was a whole sequence where had to get the "special" laptop stolen from the lab.