What type of visa do I need to live in Thailand for a year with my kids while taking cooking classes?

As mentioned previously METV is probably the easiest but it requires border bounces (go to neighboring country, and return 10 minutes later). You would have to do that every 60-90 days. Each trip if done through an agent can cost about 4000baht a piece.

You may want to consider a 6 month plan. When you are here you will talk to other people and discover what/how they do. It could be you find a like minded parent that you trust and you can leave your kids with for a day, then only you have to do a border bounce. You could find a job that does the work permit for you... any thing is possible but whatever you do it will be easier from here.

You won't be able to live in Thailand for a year on a tourist visa. The closest you will get is a multi entry tourist visa which if used judiciously will give you almost 9 months with a couple of border bounces

You wouldn't qualify for a visa for taking cooking classes though you could potentially qualify for a visa for learning Thai language or Muay Thai.

You can't do any apprenticeship as that's considered work and you must have the appropriate visa and work permit for work. Even volunteering for no pay is considered work and requires both as well.

If your children go to international school they would likely need to get education visas. If they go this route you can get a visa based on your child attending school by showing 500,000 baht in a Thai bank account.

If your kids do not go to school and are under 15 and will not turn 15 during the year you are in Thailand, they technically don't need a visa. Children under 15 cannot be fined or banned for overstay.