Years ago I recall when my lawyer told me, "Courts love therapy." So, given enough time to slug it out in court, you do have the legal system on your side. However, the extent the court is on your side is not guaranteed. It may decide to simply order counseling and little more. You need a practical strategy as you do that or else you might get counseling for your child by an inexperienced or gullible counselor that your ex chose.
You can be strategic by assessing the potential counselors beforehand, building a short list of respected, experienced counselors, perhaps also who take the payer's insurance. Then present it that ex chooses from among that vetted list. Court will like that approach since it involves
both parents.
My lawyer always told me that courts love counseling. I hope that's true with your court too. If dad wants counseling for the children and mom doesn't, I can't imagine court not ordering counseling. Dad should of course think ahead and know that mom will try to sabotage any ordered counseling. She'll want to take over counseling and squeeze out dad. She'll want to choose the counselor. She'll make so many claims about dad that counselor could be overwhelmed thinking, "Surely if there's this much smoke, there must be a fire in there somewhere."
So dad will have to make sure certain things happen... That court orders counseling for children promptly without waiting for the rest of the case to proceed to wherever it goes. Dad should offer up a short list of excellent counselors so ex must choose from among that list and not pick her own gullible counselor. Court order should state that dad is involved in counseling at least as much as mother to avoid him being shut out. Mom cannot 'fire' the counselor without dad's consent or return to court for adjudication.