In this case, "which" is being used as a determiner. "Which", like the other interrogative determiners "what" and "whose", is mostly used in questions, since they ask a question:
- Which book should I read?
and can be used after prepositions or conjunctions:
- At which time did he come?
- On which platform is she standing?
- You can see us from which window?
It is not common nowadays to use a phrase like this, with interrogative determiners in a statement, outside of legal jargon, however the format can be found in older examples. Nowadays, one would simply either
- use "the" or "a",
- use a preposition or conjunction instead,
- use a relative pronoun if you are specifying, or
- use "whichever", "whatever" or "whoever's" if not.
- You should read which book you desire.
- You should read whichever book you desire.
- You should read the book you desire
- He came at which time the bell rang five.
- He came when the bell rang five.
- He came at the time the bell rang five.
- She is standing on which platform the old beggar sings.
- She is standing on the platform where the old beggar sings.
- I can see you from which window the banner is hung.
- I can see you from the window the banner is hung.
- I can see you from the window where the banner is hung.
In this case, you can parse the full sentence to say:
Judge: And I order the mentioned child to be remanded into the care of Family Services, until the time the father can demonstrate the abilities to perform the duties of a responsible parent.