My answer is if you share joint custody this is not a good idea at all to go against the other parent's wishes. You need to have the consent of the other parent or a court order to do that. In some cases I have had parents make major decisions for their children that the other parent was not in agreement with and it actually caused them to lost custody of their children.
When it comes to decision making or custody it usually pertains to major decisions for the life of the children. For example mental health treatment, medical treatment, education, in some cases religion. In Arizona we have personal care decisions. Which amounts to for example can the child get their hair colored blue or a mohawk or get all kinds of piercings.
If you share joint custody with another parent then you have to discuss those categories of major decisions with that parent before making one of those major decisions. Certainly enrolling your child into some sort of mental health counseling would be a major decision.
I've had judges say, "Listen, you changed the kid's school or you actually moved somewhere without talking to the other parent. You moved to a city or town that is 60 -100 miles away from the current residence location." Judges don't like that because what it shows to them that the parent is making a decision without talking to the other parent about it first, then that parent is not capable of co-parenting.
So the judge says you can't coparent so I'm giving this decision making power or authority to the other parent in the hopes that they will do a better job than you have. So enrolling your child in therapy without talking to the other parent goes beyond that the therapy might end if the other parent finds out.
You are really risking your custody or decision making position or relationship with the other parent as it relates to your kids. Don't make major decisions if you share joint custody without talking to the other parent first. Of course there are times when an emergency comes up and you have to make an emergency medical decision.
You have to try and reach the other parent but if it is a life or death situation, sometimes you do have to make that decision. If your child is at risk for harm or death is imminent my advice would be call 911, call the police or call someone who can do something about it immediately. Then file an emergency motion in court immediately.
But do everything you can, everything in your power not to make those major decisions without involving the other parent first.