var parentPos = document.getElementById('parent-id').getBoundingClientRect(),
    childPos = document.getElementById('child-id').getBoundingClientRect(),
    relativePos = {};

relativePos.top = childPos.top - parentPos.top,
relativePos.right = childPos.right - parentPos.right,
relativePos.bottom = childPos.bottom - parentPos.bottom,
relativePos.left = childPos.left - parentPos.left;

console.log(relativePos);
// something like: {top: 50, right: -100, bottom: -50, left: 100}