Yusef, in my mind, the question of if the mother files a recovery order does she have to be specific about the date you relocated? indicates you have specific concerns about an actual date being known.
Your timeline is not clear to me. You claim to have moved with the children from QLD to Vic 5-6 months ago. Yet, you state the mother last spent time with the children on 12 January this year (5 months ago). She returned them to you by taxi (a long taxi ride from QLD to Vic).
You say the reason the mother does not want to spend time with the children is because the children do not enjoy spending time with her. I will not make any assumptions about this, except to note that barriers to this (strained?) relationship between the children and mother have been further increased by the interstate relocation.
A missing persons notification was made by the mother to the police 3 weeks ago, leading me to believe the mother was not informed of the move nor the children’s location.
The mother may never file a recovery order, and this would be to your benefit (more time elapse). However, if she does proceed with Court action, in my mind, far more than “the kids don’t want to see mum”, “she goes on holidays” and “I needed work” will need to be explained to the Court in terms of your unilateral actions.