Queen BB,
Under the SAFE Act, I know of no restrictions on dual employment, provided that they meet the requirements of an MLO under the particular industry environment (bank vs non-bank) that they are working in AND provided that there are no additional restrictions in your State's version of the SAFE Act.
The SAFE Act is about ensuring that MLOs are qualified, on a list somewhere (registered or licensed), and that consumers have enough information to decide (based on the info in the list) if they want that particular MLO handling their loan. So in your case, I would say that as long as the MLO has met the registration requirements for the bank and the licensing requirements for the non-bank subsidiary, you should be fine (again provided that your State's SAFE Act does not prohibit/restrict dual employment).
_________________________
I can't herd the cats anymore, so I just set up the electric fences and let them fry when they stray out of bounds.