It's very difficult. On the one hand ex wants to move for a job - fair enough as you say - but the kids have two parents who then live at some distance apart. I wouldn't push the welfare issues with social services as presumably Cafcass haven't found any real issues with your ex and that may be seen as historic (or her not coping after the break up temporarily or something) and just makes you look hostile to her. However justified, any negativity towards the other parent counts against you. But if you have social services reports/closure reports or anything in writing you can use that at final hearing.
Of course the kids should stay in their familiar environment and at their familiar school, but having seen other cases like this the courts just say - they'll adjust to the move and a new school and they need their Mother and do the best we can with time for the Father. As you say be prepared to move closer. But yes push for a 50/50 order whether they move schools or not.
It's a complete mess to be honest - it's left the kids without a school! By them saying wait till the next hearing to decide about schools/lives with. And also saying your ex can move the kids.