From the psychological evaluations and home-studies you have to show the courts that you are a better parent. Sometimes the judge will make up his or her mind before the hearing takes place, based on the information found in the psychological evaluations and home-studies.
In your psychological evaluation you need to show yourself as a happy caring parent with strong parental skills and great patience, who wants to maintain a strong healthy relationship between the other parent and the child(ren). You should be a very happy, contented person who has a concern: that the parent may not be able to properly fulfill the role of custodial parent because he or she does not want to keep you informed or included of the important aspects of the child's life, like their progress in school and or major decisions involving the child. Also you are concerned that he or she may not fulfill the role of CP in the best interest of the child because of thing she or she has done. As you explain why you are concerned about such activity, show the evaluator the documentation of what he or she did. You must show that you are a better parent while at the same time providing evidence to the evaluator showing them your spouse's shortcomings as a parent.
The same for the home-study. Not only do you show a good home-life for the children, but explain your concerns over custody...and why you would be a better parent. Make the social worker fully understand the efforts that you would make. Remember, this is some of what the Judge is going to see and consider.
You have to call him a good parent, state you are a better parent, state your concerns and tell how you would do a better job.