You can't append new elements to an input's HTML, you need to wrap the input within another element and prepend the new buttons to the wrapper element instead.
Here's a JSFiddle showing what I mean[
^], though you may need to tweak it a bit because it doesn't wrap elements correctly.
As you can see from the example, the input is wrapped within a div element, and we then prepend the buttons to the div element (before the input field). Also the innerHTML property is meant to take a string value, not an element reference.