In our case they just orded a psych eval for SD's mom, not my husband. It turned out to be a disadvantage because the evaluator never saw SD with my husband and SD at that point was very willing to put on a show to try and help her mother. Despite that the evaluator did recognize and comment on the unhealthy "emeshed" relationship that the two had.
The grandmother of SD told us before that SD's mom is bipolar. Apparently it runs in the family, but SD's mom and family will never admit this to an evaluator and it's very difficult to find documentation of these issues because mental health issues are protected personal information.
I think that it is very good that the evaluator is going to test both parties and see them interact with the child. It is extremely good that you have documentation of her bi-polar and other issues. If you have a custody evaluator, that person would most likely be the best person to give all that info to. They ask for that infor and use the psych eval. If she lied to the evaluator or the psychologist and you can prove it with the documentation you hand over, it looks very bad. But, maybe it would be good to bring it with him to the psych eval and give it to the psychologist as reference material.
In regards to the background check you did on the new husband. Did you get actual copies of the court docket or court filings? Associated police reports may also be very helpful. All of that is public record. I was completely surprised when I asked for police records about the information I got. I asked for the info on SD's mom, her husband, her family, and her old addresses (from each city and the county). Not every state keeps good records though. KY said their info was not computerized so they couldn't give me anything unless I knew specifically what I was looking for.
Best of luck. Please post back with updates.