The short answer is YES, most likely.
However, I have heard that sometimes Disney won't let you pay for someone else's meal with your credits. The principle is the same. Kid A would be "paying" for Kid B's meal with his credits.
I don't see why this is a problem because they are your credits, you should be able to use them how you want them. And in my experience, it hasn't really mattered who had what. It would just be like you footing the bill for someone else if you were paying cash.
Just saying, others have noted you "may" run into problems trying to have one kid pay for the other. However, those problems are usually centered around one person paying for someone who is NOT on the dining plan. Since all of the credits should be on your account, they will probably let you use them how you want.