The same day after the trial, the divorce is being carried out. The King and Queen are the ones who helped process the divorce seeing that the Emperor is against the notion of divorcing Elaina. Since they got involved in the process, even if Alfred wanted to try and reject it, the divorce process will continue and he has no say about it, whether he likes it or not.
And even if Alfred does not comply, someone from the mages that the King and Queen employed will force Alfred to perform it as the divorce is forcefully carried out due to the trial results. If he managed to make a convincing lie earlier, forcefully enforcing the divorce might not have been an option but because he immediately gave up and confessed to what he did, it is his fault that he is being forced to sign it.
