You can only "reopen the case" in one of two ways:
1) appeal the judgment. You can only do this if you file a notice of appeal within 30 days of entry of the judgment, and only if you can demonstrate that the trial court made an error of law in deciding the outcome of your case. An "error of law" is an error in interpreting the law - NOT in interpreting the facts. So merely disagreeing with the judge's assessment of the credibility of testimony, for instance, won't cut it (unless you can prove to the appellate court's satisfaction that no reasonable factfinder could possibly have found, based on the record, what the trial court found - an incredibly hard standard to meet). You must have objected to the trial court's ruling at the time, in order to preserve the right to appeal (unless the mistake was "plain error" - again, a very high standard). The only way to see whether an appeal is worthwhile is to have an attorney review the trial transcript for errors. If you settled the case, or if it's been more than 30 days since the judgment, then appeal is impossible.
2) file a motion to modify custody. To do this successfully, you would have to show that a substantial change in circumstances has occurred since the judgment was entered. Merely disagreeing with the factual conclusions of a custody evaluation or other mental health assessment doesn't count. For legal purposes, any findings made by the court at that time are deemed to be true, however much you disagree with them. You'd have to be able to show that things have changed, and that the custody schedule you propose now is in the child's best interests. You can be sure that the child's other parent will try to use the same evidence against you, but if they do, you can try to introduce evidence of your own to show why these claims are flawed.
It's important to remember this: you can't take it for granted that anyone else will agree with your opinions about the quality of this evaluation. You're probably not an expert, and even if you are, your opinion is clearly going to be biased in a case about your own family. If you want to make these claims, you'll need to have the opinion of some reputable expert, either to evaluate the quality of the assessment already done, or to do a new one. Family law courts put a lot of stock in the opinions of child custody evaluators, child psychologists, and other mental health professionals. If you want to challenge a professional assessment, it helps to have another one.
I won't say there's NO chance if you represent yourself, but think of it like this: representing yourself in court is like performing surgery on yourself, with no medical training or tools. It's legal, but you're likely to hurt yourself. Or, look at it another way: if you didn't know the answer to this question, do you feel confident navigating the system on your own? If this is a priority for you, it's worth consulting with an attorney about.