you might want to look beyond the major national-level events and check local prefecture or club tournaments. Japan has a pretty active table tennis scene, and some smaller competitions are much more welcoming to recreational and junior players than the big professional events.
With kids aged 10, 12, 16 and 19, I’d specifically look for tournaments that have separate junior or age-group categories, rather than open events where they would be competing mostly against experienced adults. It would also be worth contacting the organizers in advance to ask whether players from overseas can enter without being registered with a Japanese club or association.
If you already know roughly which cities you’re planning to visit, that could make the search much easier. Tokyo, Osaka, Kyoto, Nagoya and the surrounding areas have plenty of clubs and competitions, so you could potentially build the trip around a tournament instead of trying to find one after the dates are fixed.
