I'd name the woman Zoe
, and the kids Alex
I just say though - fostering really doesn't work that way. If the mother had abandoned her kids then social services would be involved, and they would remove the children to emergency care, followed by a placement either with their extended family or with properly trained and vetted foster carers. They wouldn't be left with the neighbour (except under the extremely unlikely scenario that she was already on the service's long-term foster carer's list and happened to be offered the children when family options had been considered). So you might want to re-think that part of your plot.