You worry that you will say Yes and your ex will say No and then that's the end of it, nothing gets done. Well, you have a resource, the court or possibly a court appointed lawyer for the minor, a Guardian ad Litem (GAL). How so? My lawyer stated to me simply, "Courts love counseling." So even if your ex firmly puts her foot down and states, "No way!" then you just turn to the court, probably the one that issued the custody and parenting order. We here in peer support leave the legal details to the local but experienced proactive lawyer who knows the local process and rules. You probably should have a record of the letter, email or text message so that you can be able to confirm you've already tried to resolve it with the other parent before turning to court. Again, you may want your lawyer to review it just in case so it is clearly worded but reasonable.
For example, you probably wouldn't want to say "Daughter wants counseling for whatever." That may put the ex's focus on daughter and she could be tempted to pressure daughter to state she never wanted counseling or doesn't want counseling after all. Hmm, to forestall that attempt, you may also want to first have daughter give you something in writing and dated where she asks you to help her with getting a counselor. You would hold that in reserve if needed for use in court.
Be careful to educate your daughter that her mother may resist this and pressure her. Advise her to shunt everything to your shoulders, let you get the wrath, manipulation and cajoling instead of her. She's a kid after all. Kids don't like being in the middle. This is for adults to decide, not kids. If the parents can't reach agreement — let's hope you two can reach an agreement — then let the neutral professionals decide.
However, what you don't want is for your disordered ex to choose the counselor, odds are she will select one that is inexperienced, gullible, biased or easily manipulated. And if she does find a good one she may dump him/her and seek a more pliable one. So is there a strategy to minimize that risk?
Does your son have a court authorized counselor? It sounds like he doesn't? With one parent pitted against the other and the child in the middle, that's no place he wants to be. There's a section in Richard Warshak's
Divorce Poison which describes how it's not surprising that the child, even one in his teens, chooses the aggressive parent hoping that then the pressuring is less. And the mentally healthy parent gets trashed. Well, that's not a good solution, his mother will pressure and tear down any good boundaries he may want to make or establish...
My lawyer (in USA) said, "Courts love counseling." If your son doesn't have a counselor then your court may agree to order counseling for him. If so, then how to reduce the risk of the ex controlling the selection so he gets an enabling, inexperienced, gullible counselor that she could sway to her side? One way that has worked in the past with courts is to be the first to present a short list of vetted counselors who have a good reputation of unbiased reporting to the court. (When considering Custody Evaluators, my lawyer stated to me that his choice was someone he'd worked with before. His words were, "He's like god to the courts, it always follows his recommendations." And he was most excellent.)
Once your short vetted list is proposed to the court then the other parent is to choose from among them
only. Courts can see this as both parents involved in the selection process.
What is your parenting schedule like? In my case, I had alternate weekends during the divorce process but came out with equal time. The schedule was 2-2-5-5. My ex had Mon-Tue overnights, I had Wed-Thu overnights and we alternated the weekends. That didn't work, my ex still felt in charge and entitled to disparage me as parent so now I have full custody (as Legal Guardian) and school weekdays with me.
In other words, your current parenting schedule may assign you too little time with your daughter. That's why I asked what your custody and parenting schedule are like. My county states in its admittedly powerless "parenting guideline" that teens generally do better with a "home base" with one parent. You can present your reasons to the court that your child's needs are to spend that majority of her time with you. (Again, she may be afraid to state so to her mother, so that's something you would need to handle as the more stable adult parent.)