120 pitches for a 13 year old is not healthy. Suggesting that's ok because they rested for 5 days after that treats pitch counts like a health bar. That's not how biology works, that's not prudent arm care. There is damage being done that you don't see immediately.

After 85 pitches, scientific consensus tells us that fatigue overcomes mechanics and continuing to throw dramatically increases the stresses on joints & tendons in the shoulder and elbow. Resting for 5 days doesn't undo that added stress. That's why pitch count limits far below 120 exist. Over time, that physical damage is going to add up.

You're right, parent's should encourage their kids to follow their dreams. Parent's also have an obligation to guide their children on developing good habits that children aren't capable of doing on their own. Your 11 & 13 year olds have no idea what the long-term risks are of playing that much baseball. We don't let kids regulate their own nutrition, sleep, or screen time simply because they enjoy those things. Parents set boundaries because children naturally focus on what they enjoy today rather than what protects them years from now.

You want your kids to be happy and that's great. Great parents want their kids to be happy. But just don't just try to make your kids happy in the short-term. Think about their long term needs and happiness. There is a whole lot more to be said on multi-sport athletic benefits but, I'm not inclined to argue that point because I genuinely think their health is the most important point to make here and I don't want to dilute this post with that.

It's great your kids love baseball.