The plan is very easy to use. You do need to make ADRs for your table service, but you need that whether you have the plan or not.
At a character meal, you just present your KTTW card and the CM runs the card--it deducts the appropriate TS used (in your case, 2 adults and 2 children would remove 4 TS credits).
At a regular TS (where you order off a menu), you decide how many meals you are ordering. Are you sharing with the kids? Your meal includes an appetizer, entree, dessert, and beverage. If sharing, tell the server--they will bring an extra plate/plates. You may want to order an extra beverage (and pay OOP) or water. If you order 2 adult meals and share with the kids, the CM will deduct 2 TS credits.
At CS, you decide what you are ordering. An adult meal is a combo meal or entree+side. A beverage and dessert comes with it either way. You find a seat with the kids and send DD to the counter (ok, he can sit...the bottom line is you don't have to stand there with the whole family!). He gets your order and brings it to the table. You can get 2 adult and 2 kid meals or you can get 2 adult meals and share with the kids. It's your choice.
You may end up with some extra CS since you have concierge breakfast, but so what? You still came out ahead on $.