She may be totally different in a new environment and settle down for a bit at her friend's place. I think it's worth a shot. We had a family friend stay with us for 6 months to finish year 10 when her family moved away. She didn't have the troubles your daughter is having but just to let you know that these things do happen and it doesn't mean you are abandoning your daughter.

Perhaps let her know it's a temporary thing as you want her to move with you but you understand her desire to finish out her schooling at her current school. If things don't pan out in the short term, or by the end of the year then she can move with you and finish year 12 at Woodend. By which time your second baby will have arrived so you will be able to move again, she will have had a break and perhaps things will be smoother. The change of school could also be a benefit to her to break her current patterns.