Hi & Welcome to the DIS
I am always looking for ways to save and am always on a budget. Here are a couple of my suggestions. If driving, bring along a cooler and use it in your room to keep drinks &/or snacks cold. We took a case of water and a 12 pack of soda. We never used the refillable mugs and we didn't miss them. Every night we would drain the cooler and refill with ice and add what drinks we would want cold the next day. Sounds like a hassle but honestly it took about 5 minutes a day. (If staying at a value there is not a fridge unless you request it and it cost $10 a day)
We purchased milk, cream for coffee, cheese sticks, OJ, etc at home and brought it down with us in the cooler. I also pre measured cereal into baggies and brought along syrofoam bowls. We also had crackers, granola bars and poptarts for snacks. I packed plastic utensils and brought along some plastic cups. We ate breakfast in the room while getting ready or while waiting on the bus. We stayed at POP and there is not a coffee maker so we brought ours from home. I pre-measure the coffee and bagged it at home. I also purchased sugar in a round dispenser and brought my mugs from home. I would wash them out every day...very little hassle and I loved having my french roasted coffee every morning and not having to go to the Food Court. I hear Disney coffee is the pits anyway.
We did do the
DDP (We loved it) so we would eat an early lunch and then use the table sevice for dinner. You also get a snack each day. We had plenty of food and felt like we got to enjoy whatever we wanted because of the DDP. It is well worth it to me to be able to eat so well and have it already paid for...no worries adding each item up at the rest every meal. Also tax and 18% gratuity is already added. Since you have 2 little ones they would just be $11 per day each on the plan. Believe me that is a deal!!!
I would also give each child a set amount of money to spend. My DH & I told them we would buy them a hat and an autograph book on the first day. Anything else they purchased had to come out of their money. Tell them to look at each shop and think about what they spend the $$$ on. When it is gone - it is gone. My kids were very careful to think about what they spent THEIR money on. SIDENOTE: If you are driving there is a Disney outlet store somewhere close by (search here on the boards) and we found some fantastic deals there.
Make sure you buy your film, memory cards, batteries at home...very expensive at Disney.
Also make sure to pack any OTC meds like asprin, pepto, cough or cold rememdies from home.
We were on a budget and had the time of our lives. We never felt strapped - we ate like kings, purchased souveniers, and had a blast. You guys will too! If you are doing the DDP make your ADRs soon.
I think you may be going during Spring Break time...get some strategies for touring the parks and utilize your FPs. Get up early and hit the parks at opening to beat the crowds. Rule of thumb...when in a crowded line...go left. Either you or your wife grab a FP from one attraction while the rest of you get in line at another.
TIP: Make sure you take everyones ticket to the FP machine. You can use you FP after the time has expired (just not before it starts) and once the time starts you can grab another set of FPs.
Have fun!!!!
Hope this makes sense and helps a bit. Let us know how it goes or if you have anymore questions.
. It's Disney's newest Value Resort and I think not only will your kids love it, so will you. If you're wondering if you need a car ( assume you are flying) ask for a reservation that includes the Magical Express for your transportation back and forth from the airport and WDW. 
for night-time when we're back at the room. I've brought a whole box of my kids favorite cereal, crackers and Easy Cheese,graham crackers, etc. When you make room for snacks in your luggage, you know you'll have room for any souvenirs.
