How much influence does a Guardian Ad Lidum report have in making a judgement in a child custody case?How easy is it to dismiss?

Given that no one here knows the specific details of the case, no one here likely can answer with any certainty the question posted: "What are the chances that the father will win the dispute in regards to the GAL report being thrown out?"

The guardian ad litem (GAL) likely is appointed to represent the best interest of the children. The GAL should have done a thorough investigation and wrote a report to the court. The GAL may have made recommendations to the court. Whether to accept or reject any of those recommendations is up solely to the court.

The father and mother, through their attorneys if they are represented, should have an opportunity to present their sides of the case to the court.

It is not unsurprising that the party who thinks a GAL's recommendations favor the other party to oppose the GAL's recommendations.

You should review your specific facts with your attorney to see what legal options you have. Keep in mind that once a GAL's is filed, that may means the hearing is likely coming up in a few weeks or days. That is, there may not be much time left to gather evidence to support or dispute whatever is in the GAL's report.