It took a decade of martial arts practice and the great fortune of my career at the CIA to ever consider doing BJJ and judo at the same time. Never have I ever done more than one at a time otherwise.

Depends on the adolescent and the gym. A kids program can simply be superior in terms of instruction and organization in which case any combat sport would do if their program is good. Because if this my first reflex is judo. You get more culture baked into the lessons and atmosphere because you get the direct lineage from the founder of judo, the oversight of the IBJJF, and the national judo foundation to create a more consistent style of what a judo class does. That style emphasizes discipline, practice, and respect. You probably get more interactions between young people, adults, and elders. BJJ has a whole lot more “don’t call me professor, just call me X” and “check out this neat neck crank.” It’s for swashbucklers. That’s cool, awesome, and dare I say effective (for self defense), but for the developing brain it seems desirable to get that sense of respect and community that judo more readily provides. If they’re not going to listen unless it’s rough and tumble, they might get bored of judo - it’s easy for me and my brain to know that I’m building a really sick and comprehensive grappling game by going to judo class and practicing with less intensity. However, I might have been bored to tears earlier in my life. If child me had 3 peers with whom I form rivalries in BJJ or muay thai I’d be happy to go all out with them and suddenly I have buy in

You can find muay thai for children. You can also find full contact muay thai for children which feels very bad to watch with my soy, effeminate, western sensibilities. And again, if a gym’s children’s program is superior then you’re going to get more discipline, practice, and respect. They’ll do no head contact, bag work, and learning how to use pads. By the way, holding pads for your child is a WONDERFUL way to bond. You don’t need to practice muay thai to know this skill. It’s akin to playing catch. Except even when they’re edgy, rebellious teenagers, knowing that you’re there to help them conduct their violent energy into something constructive until the endorphins pop out of their neurons could be everything. All it would take would be one time when they’re angry and guilty but you say yes to holding pads to demonstrate loyalty, love, and respect that they’ll remember forever.

I think combat sports change the game for a child in terms of dealing with anxiety, fidgety ticks, energy that needs to be expressed, not knowing what to do with your hands, talking to adults, and being handsy. If you can deal with being pinned to the floor by a 100kg judoka, you can deal with drama in the hallway. Go with the gym that makes logistical sense (cost, distance from home) and has a good kids program. I’d start with looking for judo for general development, but if the child wants to go fast then BJJ or muay thai might be more their style.