Even if you didn't upgrade, I'd think 4 days of nothing but counter service food will become a bit tedious and you'd start trying to book sit down restaurants. The difference in price for 4 adults in 2 kids over the course of 14 nights seems quite reasonable, it's less than 12 pounds/16 dollars per person per night.
I'm sure you'll get tons of advice about how best to use your credits. Here are some of the most basic suggestions
Breakfast is usually cheaper to buy out of pocket than lunch, and lunch is cheaper than dinner, so it's best whenever possible to use your table service credits for dinner, counter service for lunch, and either pay out of pocket for an inexpensive counter service breakfast, or perhaps snack credits.
If either of your kids want to see princesses, it takes 2 credits for each person to get a meal insider Cinderella's castle...but only 1 credit per person at Akershus in the Norway pavilion at Epcot.
Some meals might include special seating for events - examples include eating at Tusker House in Animal Kingdom (a character meal, only 1 credit) could include special seating at the Rivers of Light show at the end of that night. Or going to hollywood and Vine (character meal) or Mama Melrose's in Hollywood Studios might get you a pass to see Fantasmic. It's like getting an extra fastpass. BTW both of those parks include nicer restaurants that offer the same seating option, but they use 2 credits (Tiffins at AK, Brown Derby in DHS).
Many of the counter service meals are still HUGE. You might find 2 people can split one, which will allow you extra counter service credits on other days where you might need them, including your checkout day, since you get meals for each NIGHT of your stay, but the meal credits on your account are valid until the end of your checkout day. It also might come in handy if you do decide to do a Signature restaurant that requires 2 credits for each person.
To that end, many side items in counter service restaurants can be had for a snack credit. So if you're splitting a counter service meal between 2 people, getting a side item on a snack credit can stretch it further. Probably one of the most extreme examples - Flame Tree BBQ, for one counter service credit, you can get a sampler platter that includes chicken, ribs and pulled pork ($19), and for a snack credit, you can get French Fries topped with pulled pork and cheese ($6.79), and that would probably be enough for 3 people to share.
Some people do the same thing for snacks, get a huge cinnamon bun, probably as big as one of your children's heads, two people can nosh on that easily. Or a giant ice cream-cookie sandwich at the Plaza, just one snack credit but I usually split one with one of my daughters.
If anyone in your family is a coffee drinker, pretty much every drink, of every size, at every Starbucks on property is a snack credit.
Everyone in your party staying in the same room need to be on the dining plan...but not everyone needs to use the dining plan at the same time. If there's a meal where one person or more isn't very hungry, then as long as it's not a buffet/all-you-care-to-eat/prix fixe meal, they can just have an appetizer, or something so inexpensive that it's worth paying out of pocket. Depending on the management of any given restaurant, they might even let an adult order off the kids menu and pay out of pocket. That saves you a credit for later.
If your family is big on popcorn, there are souvenir buckets you can buy (out of pocket) that are refillable for your length of stay and each refill is significantly cheaper than buying a whole new disposable bag/box of popcorn. You wouldn't be able to use your snack credits on the souvenir bucket, and it wouldn't be a good use of your snack credit to use it towards refilling the bucket. But getting the bucket affords you an inexpensive snack out of pocket so you can use your snack credits on other more substantive snacks later.
If one adult member of your family is not big on alcohol, management is usually OK if that person orders a beer or wine and gifts it to someone else at the table who IS big on alcohol. This might mean you have to buy a soft drink for that adult out of pocket, but you'll still make out a little better having received an adult beverage that would cost more out of pocket than a coke.
I'm sure other people will have better examples if you choose to get the plan. But in your case, I think it's worth it.
