I don't believe Jo. Co. has LCM, but you should probably check. I've heard of people requesting certain mediators for a change of custody, but I think that's really up to the judge. Getting a mediator who is a LSCSW or psychologist will be more difficult to find than an attorney I'm sure. Keep in mind that even though your order says that, you can file your motion to change custody and set it for trial. If she asks to attend mediation, you can then attend, but I don't think I would ask for it. I know one of our members here had language very similar to yours. Custody was changed and they never even attempted mediation. That's because, like I mentioned earlier, mediation is great for couples who can actually work together, but for highly conflicted parents, it is a complete waste of time and money.
It sounds as if the kids genuinely want to be with you more, which will weigh in with the court, but they need to have very good reasons for doing so. Just because dad is nicer wouldn't be a very good reason to me. But, something like asking for help on homework and Mom won't take the time to help, but Dad will, is a good argument. If you are ready to spend the money and put your kids through a court battle, just be prepared for all the junk that goes along with it. I'm not discouraging or encouraging you, I'm just telling you to be prepared for the emotional toll it will have on everyone. If it is worth it, then go for it.
Now, I do have something else I might throw out there. Courts generally try to order what is "typically" occurring. So if you ask your ex to have the kids for additional time routinely and you start to exercise a parenting plan that places the kids with you more, then you could argue that you are already acting as the primary residential parent anyway, so the change for the kids would be very small. Good thing.
