I'm hoping more people might add to this but I am getting the DDE next month because I also have 4 kids and 2 trips planned, with possibly more. It sounds like we have similar eating out styles (one good TS meal/day) so when I did the math it was a definite savings. The DDE can be picked up at Guest Services with your AP for $60 and is good for a year.
You may want to call and ask about adding it to your paid reservations to see if they will change it, I'm not sure. The 18% tip is now included (added automatically) when you use the DDE. Still, when you figure that on an average $150 dinner, you save $30 right there. A few meals and it's paid for.
There is a list of participating restaurants listed somewhere that might be helpful.