Was this a Hague trial or family court custody trial? The former should have played out long ago and if he is appealing based on the Hague tenets, then this goes against their signed international agreement and should be up for appeal, as many times as it takes, and cannot be considered a "final" decision.
It was not a Hague case in that it was not litigated under the Hague Convention but rather domestic Italian law.
Liam lived in Italy before he lived in the US. There was a several year old Italian custody ruling and ongoing custody proceedings in the US that were not going well for the mother at the time she took Liam to Italy.
Because of the prior Italian order they refused to hear it as a Hague case so it became a custody and relocation case under Italian law. I don't know all the details and history well, but I think it should have been heard as a Hague case. Liam lived in the US for most of his life.
Legal details aside, Italy itself called the mother unfit and that leaves the father as the only fit parent. On the one hand it disgusts me that they'd give custody to an uncle over a fit and caring father. On the other hand it doesn't surprise me. Family law has been increasingly weakening, when not outright destroying, parental rights. Now days there's almost no such thing as parent's rights. It's not about the parents it's about the children. The only rights a parent has to parent are often those conceded upon the parent as the result of the child's right to be parented by their parents -- which is just one of many children's rights (privacy, education, freedom of religion/association, language, nationality etc) and one that is increasingly not seen as critical. Which is not to even begin with the child's right to have their wishes or voice heard (usually through their government appointed representative and spokesman.)
Italy decided that the child's other rights (privacy, language, nationality, association, etc) were more important than his right to being parented by his father so they gave him to his uncle. Before long some random person will be able to grab a baby in the hospital and hide it for a while then argue that they have "bonded with the child," are wealthy and can provide a better life to the child and than the biological parents and win custody all while the judges, lawyers, social workers and psychologists, who just earned a lot of money for their role in the multi-year litigation, congratulate themselves on their "modern and progressive" view of children's rights rather than believing in antiquated and barbaric ideas like "parental rights" that treat children like property (and don't require extensive psychological, sociological studies or long drawn out court battles.)