2-3 tree: Sum of leaves in a given range
Storing the sum for internal nodes is a good plan.
For every query you also need to search for the two bounds of the interval, and find the leftmost and rightmost leaf with elements in the interval. (The bounds themselves do not need to be in the tree.) The two search paths will split a a certain node. Continue there. While searching for the leftmost leaf you include all sums to the right.