Do you just have the transcription of the 1911 entry. You would need to look at the handwriting on the original to see if it is more likely to be a mis-transcription of "within" (or "under" as Lesleyhannah suggests) - but it does seem quite possible.
It does seem odd they were getting help from the poor law union. Perhaps it had something to do with her being his step-daughter rather than his natural daughter. Perhaps he was a very cunning assurance agent who knew how to work the system. Perhaps she had mental health problems that made her a special case...endless possibilities. But a bit of digging into the Poor Law records at the archive may uncover something for her (if you are very lucky) or at least some explanation of who was entitled to help and why.
Or perhaps another post on Rootschat asking if there are any poor law experts who may have something to add might be worth a try.
Not sure about the other child. Presumably before her marriage he would have been called Jackson - but they may have used another of the surnames - Langley, Dono or even Austin (where did that come from?). And he may have died but could by then have been using any of these names
Good luck
Milly
