Practically, if the furniture in the “work” home is what you and your ex have both bought, then you are free to take it with you – well half anyway. And I would suggest that for the children’s well being comfort in familiar furniture would be appropriate. So I would make this clear, And I would say that as you’re moving due to him, he should pay for the removals.
Do you have a joint account? If you do close it and remove the money so he cannot accrue debt. THIS IS IMPORTANT.