I'm sure Cal would not have hung on to the child. He only gave her a scornful glance when he came across her the first time and didn't help her until it benefited him. Hopefully her mother survived and she was reunited with her.
As for Rose's mother, I agree that Cal would have supported her, they seemed to get along and had the same ideas about class, and eventually he would have found a rich widower for her to marry.
If Rose's mother didn't recognize Rose's name on the survivor lists, you'd think she would have recognized her when Rose's work as an actress started making the rounds. Not sure if Rose was a stage actress or a movie actress, but if Rose's mother ever saw a photo of her she would have known who she was instantly.