but I found the idea of the Domme wanting the Mother to take the place of the son (or daughter) to be hard to believe.
What you wrote below was basically what I was getting at.
The mom, at first, tries to offer the Dom money. But the dom sensed an opportunity. She would rather have prim & proper mother than the son or daughter. That's why it makes sense to me that the Dom agreed to stop seeing the son/daughter in exchange for the mom.
Also, the dom is professional. It's not a shady thing. She's an absolute professional who operates a small studio where she charges clients by the hour for her services.