$1,000 a month for tiny room, bedbugs, seedy surroundings in the Mission
sfgate.com
sfgate.com
So, moving to a new area means that she'll now have to add an expensive and long BART ride into her budget which will probably negate any savings. Plus, she'll loose any childcare resources she currently has established with friends that live in the area. There may/may not be jobs in the new area but she won't be able to get any of them there because she lacks the personal relationships with the immediate surrounding community to get a new job.
Moving is also an expense she can't afford, hence the SRO that doesn't require a deposit. If she had moved in the past it probably was from an SRO to another SRO with most of her belongings being things that could be gathered into a friends car or walked down the street.
Also, living in SF provides a /much/ better future for the children over Oakland where a residence in her budget would probably be unsafe to walk outside at night.