When you go to the tournament they'll be able to sign you up with an ID card, every player needs one and it's free. (Playing in the tournament is not though) Keep that ID card/write the number down. (Once you connect it to an online account you can pull it up from your phone via the website) You'll need it whenever you play in a Pokémon event. If you or a child ever gets serious, that's how you track points towards your World Championship invite.
Pre-release tournaments are different than normal ones as they are the only official sealed event. They occur roughly every three months. Everyone gets one of four pre-built decks, plus four packs. They then build a 40 card/4 prize deck with only the cards pulled from the pre-built and the packs. These make great first tournaments for kids as everyone is on a level playing field in that the deck is built with what you get there, plus no significant prizes are on the line so they tend to be much more casual. That's assuming the kid is old enough to enjoy playing for 3 hours or so without taking away from the enjoyment of other participants, sounds like the youngest might not be ready for a formal tournament and that's ok, take him to a league instead until he is a little older. I'd recommend taking the older one though for sure if he is able to enjoy that type of event. One thing to note, it's usually worth it to call ahead for Pre-release tournaments as they do have a limited number of kits. Some offer pre-registration and take advantage of that if you can. It's no fun to show up and they sold out. Just as an example, there are three shops in my local area running a pre-release. Two have been running for awhile and have 50-60 kits, more than enough. The third is brand new and only received 16 kits. They are going to sell out.
Do you have any leagues near you? (
https://www.pokemon.com/us/play-pokemon/pokemon-events/find-an-event/ to check) I highly recommend finding one to play casually at, as much help as we can be on a forum there is just something about talking to someone in person sometimes really helps. These are a great way to meet other local people who play the game, get tips. Depending on the average age of the league it's a good way for your kids to start playing seriously, but with the benefit of being able to leave whenever you need to. At my league there are some parents that bring their kid for an hour or two since that's all the kid can handle or they have to get there late to make sure the family gets dinner together, then there are some that stay the entire 3-4 hours every week.
Most leagues play standard regularly, but sometimes people will play expanded. Mine at least are understanding of new players so if you don't have a true standard deck due to only having older cards that's ok. Once you've played awhile you'll acquire more and be able to build a standard deck. (The prerelease will be a good way to get a bunch of standard cards!) If you have format questions let us know. Current standard format is PLC-Sun&Moon. Guardians Rising will be legal on the third Friday after release.
If you have any other questions please ask. It can be a little overwhelming at first, but it's a great hobby and one that the whole family can enjoy together. Once you get the hang of it things come easily.