Mrs. Sterling from Mommy IS Rhoda from the 1956 film version.
See She's Just Hiding on the YMMV page. The rain slicker she was wearing on the pier got charred black, but it protected her body as the lightning took the path of least resistance on her. She splashed into the water, washed ashore on the other side, found her way back into society and feigned amnesia to avoid the Penmarks being able to realize her survival, let alone trace her. Adopted and raised by a different family, she eventually grew up and became Mrs. Sterling, mother to Jessica Ann, at which point she would resume her killing ways as she lived vicariously through her daughter and wanted Jessica to have everything the same way she wanted for herself as a kid. Dr. March from the 2018 version is Rhoda Penmark.
Was she really fooled by Emma's acting as a normal girl? Probably not. She even made the overly ham-fisted joke about how she was just like Emma when she was a girl. If Rhoda survived, she has since learned how to blend in with society better and can carry out a normal life.