I think The Mother was called into being by the bomb test. She 'gave birth' to BOB. But she exists in different forms. She is also MIKE. She possessed the shoe salesman who chopped off his arm to get rid of her/it. The arm turned into the little dancing man. The little man turned into the tree. The face and mouth of the tree are similar to the Mother's face and mouth. Mother/ MIKE wants BOB back in the lodge with it. Mr C receives a message just before he kills that girl in the motel room, saying that BOB belongs back in the lodge with MIKE. The message rattles him. He shows the girl a picture of The Mother's face on a playing card. The wants to know if The Mother/ MIKE has hired these two people to kill him and send him back to the lodge.
Inside the lodge MIKE/ tree/ arm, first appears as the white statue of a woman then turns back into its tree form (further convincing me that The Mother and the arm are the same being). The floor goes crazy and Agent Cooper escapes the lodge. The Mother/ arm goes after him. Agent Cooper appears in the clear box then moves on. The Mother / arm appears after him. It is following. It kills the young couple as it is made of and for violence and fear. The white Mother figure' strongly resembling the white statue in the lodge. Agent Cooper goes through to The White Lodge (?). There is banging on the door. The Mother is following after him. Naido stops Agent Cooper going through the box on the wall. The numbers on it are wrong and would send him to the wrong place? The banging continues. They go into the roof. Naido flips a switch and is blown off the roof. She sacrifices herself. As she flips the switch the banging stops. Naido has given Agent Cooper time to go though the wall with the right numbers which he does. "Mother is coming," says the new lady, as the banging starts again. It is still following.
Agent Cooper becomes Dougie. Dougie is helped at various points by the one armed man, who always appears to Dougie still in the lodge with the zig zag floor around him. He is also helped at one point by tree/ arm/ Mother. "Squeeze his hand off". A violent suggestion in keeping with this character. This entity does not appear in the lodge setting, it is in the world with him and pops out of the pavement. Cause it followed him through. It wants to help to return BOB to the lodge. I believe it then travels to Twin Peaks and looks for someone to possess. At first it tries Jerry Horne. They tussle in the woods for a couple of days. It gets hold of his foot but Jerry fights it off. Jerry runs from the woods and in the very next shot we see Laura's mother in the shop getting upset and experiencing great foreboding. When we first see Laura's mother she is watching tv and the show is progressing normally. The next time she watches tv it is repeating and crackling. She is now possessed by The Mother/ MIKE/ the arm. In the bar we see beneath the mask. It wants BOB back in the lodge so will help Agent Cooper against Mr C.
Thats my interpretation. Do you think anywhere close to the mark?