Without being able to fully evaluate the kid's domestic situation, it's difficult to pass any judgement as to whether or not he should be prevented from ordaining in Tibet.
If I were the one determining this, I would assess the mother's judgement, and if she has shown a history of poor decisions then I would assume that this decision was not made for the child's best interests. If my impression of her was that she was rational and loving, then that would give me confidence in her ability to make proper decisions for her child.
We need to determine the risk of this decision on the child's welfare-- which we don't have sufficient information about as it's a fairly novel situation. What could happen if he goes to this monastery? The facilities may be inadequate, and he may contract some sort of illness. He may suffer some sort of psychological harm from indulging in fervent religiosity at such a young age. But in the end-- living at a Tibetan monastery at 15 sounds like a rather enviable youth to have: he'll be able to learn the culture, the language, the religion.. perhaps he'll grow up eccentric but I'm not convinced that such an environment can be confidently said to be 'harmful' to a child.
"What holds attention determines action." - William James