I agree. If you are going to use the middle name as her "official, legal" name, then I would spend the money to do the change. You don't have to do it tomorow
I think it's important to have the names match on all official documents. It will be important for the kids as adults. Who knows what this "ID-crazed" world will be like in 20 years? Let's do what we can to hopefully lessen a future burden.