We have 3 kids (2 are the same age as the OP's...7, 5, and 3.5) and we did the dining plan in May and it was FABULOUS for us!
First, remember that half of the plan is counter service and snacks, so these are a non-issue I would think. Second, as other have said, character meals count for table service...and now matter how squirmy your kids are, if they are Disney kids, they will love a character meal, right? We actually used 3 of our table service meals for character meals. We also had 3 "nice" table service meals (Wolfgang Puck's, Coral Reef, and 50's Prime Time). Yes, these were a little long for our kids, but remember that the servers at WDW are used to little kids and they accommodate beautifully. The Coral Reef was easy b/c of the "view" of course...but at the other two, the servers did a great job of keeping the "fidgets" out of our kids. The other thing we often did was have our main meal (table service meal) at lunch. This gave us a nice break mid-day, allowed us to still walk off all of that food (as opposed to going to bed completely bloated), and the kids were not so tired that they couldn't make it through the restaurant. When we had a dinner table service, they were already so tired from the parks all day, that it was asking a lot of them to have "restaurant manners." Yes, using ts credits for lunch instead of dinner is not as good of a value, but it still worked great for us.
All in all, we are great fans of the dining plan b/c it allows to try places we would never pay for otherwise (like Puck's)...and you know up front how much you are paying for food.
Also, considering the
DVC aspect (and that you hve a kitchen or at least studio), this REALLY worked to our advantage. We went to Artist's Palette and could get FULL SIZE (i.e.: the large, family size) bags of chips, etc. and kept those in our villa for snacks for afternoon breaks or for evening when crashed out and watching some tv.
And probably the best thing we did was use counter service credits at Wolfgang Puck's Express for pizza (Yes, you get them to go). DH stayed with the kids at "home" while I zipped over to DTD and picked up all of those personal pizzas and desserts and we all had pizza at home. We did that twice and all loved it.
There are tons of opinions on the dining plan out there...my overall advice is to try it once...then at least you'll know one way or the other for future trips...
P.S. If your kids are not great at restaurants, you can "play" restaurant at home. You or DH can pretend to be the server, take orders, etc. My kids LOVE this and it also helps them learn about restaurant behavior.