Wondering if there would be grounds to re-evaluate at this junction? The main reasons for them staying with their father in the family home were to provide stabilty, the least disruption to them yes? If he is now planning on moving which means he intends to place this upheaval onto them, change their schools, take them away from their friends and mother – then it wouldn’t be unreasonable of you to want to make sure this is what is best for them and thus put in an application for a prohibited steps order, so that his plan and your plan can be conisdered and the best outcome for the children realised, to stop him from just going a head.
I would call Rights for women asap about this and talk it through, and WA helpline to discuss it; and DV Assist as they could help you get the PSO x