LARPing with Kids Only Works with Full Buy-in by the Administration
I 'play' in a LARP that's been running since at least 1998. In that time, players have come and gone, and players have paired off and started families together.
From the beginning, the administration of the LARP set forth rules that players had to be at least 18+ in order to play all aspects of the game (roleplay and combat). However, players as young as 13 could also play, but they needed a signed parental consent form and always needed to have an adult guardian with them. Furthermore, the participation of players 13-17 was contingent upon their own ability to play in a safe way. For a lot of players in that younger bracket, this just meant somebody had to agree to 'watch' them when they played by being somewhere within the same general area (in other words, they required no actual supervision); for others the standard was for them to always have a battle buddy who wasn't ever more than 20' away. The latter was primarily needed for ensuring safe combat rules were followed.
Now with regards to children younger than 13, generally they may only participate in the roleplay areas of the game and need to have adult supervision. Again, some kids need a lot of supervision, others really don't.
You may have noticed that above I put the word play in quotes, I did this because right now I have a 4 and 6 year old. It's a lot of work for us to get them to and from the camp to play, so I generally skip most events (I probably go to 1 event a year).
On the occasions that I do go, the overall administration is helpful to allowing us to freely roam the roleplay areas without any issues. One key spot of the game is The Inn and absolutely no combat is allowed at The Inn, not by monsters or players. This is established both by in-game lore (no villain would ever risk the massive response that the in-game justice system would respond with by attacking The Inn) and out of game rules result in players being sanctioned in some fashion for breaking this rule.
Players can 'train' meaning they're being extremely cautious about their combat and not aggressively trying to win, but in general they're not creating aggressive situations that can turn dangerous if someone trips over an active 4-year old. This is fun for young kids because they can 'train' too.
Furthermore, at some point in the last decade our game added what they call 'Cautious Combat' trails which young children can participate on as well as players with physical disabilities. These are adventures run with all the normal elements of a trail (obstacles, roleplay, puzzles, and combat), but all NPCs on the trail understand that combat is done in an extremely slow fashion and just meant to allow the players to win. We just ignore the rules for these combats and let the players have fun. This was also a great way for me to participate in the game a couple years ago when I was recovering from a broken ankle.
Cautious Combat trails are coordinated between players and hook characters. A player group can simply ask the hook for a Cautious Combat trail and it will be done. On the very first scene, the hook will convey the change to their crew by simply shouting 'Cautious Combat!' and it's established for the rest of the trail. Easy.
Cautious Combat is not an option for big battle situations and small children may not participate in these outings, but often there are a few players who won't either. As a parent, I simply take my kids home at this point (mostly because it's near the end of the day and they're getting cranky), but others parents can ask one of the players hanging back at The Inn to watch their kids while they participate.
To reiterate, this only works with full buy-in by the administration. The reason for this is that a tone needs to be set that carries down to the player base. Kids who are 13-17 are going to need consent forms for insurance reasons and they need supervision commensurate with their specific needs.
Kids younger than 12 need a player base and administration who understand their needs are different and create an atmosphere that's safe for their participation. This means a creation of safe spaces for them to be (i.e. The Inn, Cautious Combat trails) as well as a player base mindset whom is willing to help with the load (i.e. various adults agreeing to provide supervision as needed).
Ilmari raised a concern in the comments about the tone of the game and again that is an administration element. Our game is primarily a high fantasy game, demonic sacrifices happen in big battle situations, they're not happening at The Inn.