I recently went through a divorce. I did not have the experience you described with my partner, but we did indeed go to trial. My state is a no fault state, and as stated above, that does matter. I do not believe that Poly issues will be brought up unless these issues immediately effect the children. You do not give enough details of your case to really get further into it than that. But, if there is no concrete evidence that your lifestyle effects the children negatively, it will not be brought up in court. For example, I suspect my ex is a functioning alcoholic. He was verbally and emotionally abusive, but there is no way to prove that. He has not been treated, I never involved the police, and there is no record or evidence supporting my suspicions. These things were not brought up in court. The court is mostly concerned with the health and welfare of the children in my experience. They are much more likely to be concerned about whether or not the parties are paying support, making visitation, and providing a healthy and supportive environment for the children when they are with them. Get a good Lawyer. IF you do not think that you will be able to work things out in mediation with the help of lawyers, than get one experienced in trial work. I can not express this enough. I retained an amiable lawyer at first, and had to retain a trial lawyer when it became clear that mediation was indeed not going to be possible. It was a very costly mistake. Trials are expensive, if you have any thought that it is headed there get the best trial lawyer you can. Mine was excellent.
I think this needs to be said. Divorce is very hard on all parties involved, but it is especially hard on the children. It is my personal belief that it is best to keep romantic partners away from the children for a good length of time in order to give the kids a chance to come to terms with their new lives. Bringing another person or people into the equation only seems to cause confusion, and more anxiety when the child is simply trying to comes to terms with the fact that mom and dad are not together anymore. I did not date until my divorce was final. It was very difficult to wait that long, but it was the best choice for me and my kids. I have been dating for a little under a year, and I have yet to find someone special enough to introduce them to. I think that I will wait at least a year after meeting before I make those introductions. This is what I have chosen for my family. Think through what is best for yours. I also can not stress the importance of support. Get a good therapist, form a good support network around yourself, and try not to bring your divorce into your new relationships. I wish you the best of luck.