If he takes you to court, he will have to pay so if he is the one pushing for it, it is definitely best if you let him be the one to lead it. That doesn’t mean he will get what he wants, both sides will be taken into account. Maybe explain to him that if you have a court order the days he ends up with (which may not be what he wants!) will be set in stone but if you sort things through mediation there is more flexibility to adapt as things change. However, my new partner has a court order and his ex is still making things very difficult but having the order helps because there is only so much she can do, as it is legally binding. If you really can’t work things out by discussing it, a court order at least (in theory) prevents constant disagreements over childcare arrangements so there are some benefits if you have reached the point where being amicable is no longer possible.