When a draggable attribute is enabled on a parent element() I cant make contenteditable work on its child element (<
It makes sense that the draggable and contenteditable properties would collide. contenteditable elements, like any text field, will focus on mousedown (not click). draggable elements operate based on mousemove, but so does selecting text in a contenteditable element, so how would the browser determine whether you are trying to drag the element or select text? Since the properties can't coexist on the same element, it appears that you need a javascript solution.
Try adding these two attributes to your anchor tag:
onfocus="this.parentNode.draggable = false;"
onblur="this.parentNode.draggable = true;"
That works for me if I add it to the tags in your jsFiddle. You could also use jQuery if it's more complicated than getting the parentNode.