Welcome to the site, Diamond Dogs. You will find countless threads on this topic. I'll give you some of my perspective...
I have three kids, my youngest is still playing as a rising college junior. I have coached HS ball for several years and have coached travel ball across ages from 12 - 18. I have also coached summer college ball and am asked on occasion to guest coach showcase teams. I do occasional contract work as site director for one of the big youth tournament organizations and have done so for about ten years. I just worked one this past weekend. I had ages 9-13 at my facilities so this should resonate with you and your kids. I really enjoy being around the kids and trying to provide a great playing environment for them. But FAR too many of the parents and coaches have gone so far overboard it is unbelievable. I could tell you crazy stories for days from these events. They are clearly pushing their kids to be all about baseball and putting way too much pressure on the kids to perform at a high level right now - yes, even at 8 and 9 years old. I have seen it only get worse over the years and the younger the players, the worse the coaches and parents' behavior is. Of course this is a generalization. But it used to be I would enjoy the many great parents and coaches and tolerate the difficult ones. This has shifted to the point where I have to seek out those parents and coaches who have a reasonable sense of balance in mind for their kids. I left this weekend wishing I had a clear path to trying to influence this trend. At least I can talk to you here.
Always remember that, as much as your kids may love baseball, in the end, it will not define them. Focus on what kind of person each is off the field. What other interests do they have or can you introduce them to? They will grow and change. They may continue playing baseball or they may take up different interests. They may get hurt, get a girlfriend or get beat out at some level, no matter how hard they work at the game. Be prepared to support their interests, whatever they may be. In some cases, I think balance is something that even may need to be forced to an extent. We told our kids they had to be involved in one or two outside activities, no more and no less, at a time, their choice. Told them to pick a sport or music or community participation or some other hobby. Help them be well-rounded. Help them see how much the world has to offer. Make sure part of the balance is to fulfill their share of responsibilities around the house as a member of the family. And sports is no excuse not to do so. If they are gifted enough and have the desire to excel at one in particular, gradually increase time toward that activity as part of the big picture but continue to insist on balance and new experiences.
Yes, at some point, a young player may need to spend more time outside of the regular season (whatever that is anymore) in order to continue to compete. The equation is different for everyone. What is the individual's talent level? What is the competitive environment - how good is the HS program, etc.? But it sure as heck doesn't have to happen before they are twelve or thirteen. And, even then, there still should be balance. If the kids are in a school environment that allows them to participate in multiple sports and they want to do so, let them. If they are talented enough to continue playing their favorite sport, there will still be enough time to hone their skills in that particular sport. Meanwhile, there is usually plenty of benefit from playing the second or third sport or from taking a break from team sports and doing something else.
I've had dozens of kids tell me they love baseball and want to play it all the time. I've become pretty good at reading a kid's voice and asking a few exploratory questions to determine sincerity vs. influence. There are instances where it is 100% sincere. There are far more instances where there is a significant amount of influence by parents and coaches who have the kids thinking they have to play all the time to "make it". And in many of those instances, the parents have brainwashed themselves to believe it all comes from the kid. Thus the need for appeals from folks such as Smoltz.