From what I understand (after looking twice), I think it would come down to this:
relative positioning for the images is a misunderstanding and
absolute was meant. Which will give the issue of not being able to position the buttons to the right of the slider because it then has no width (or height). But not all the images need to be absolutely positioned, I think. Leave the first one relative and the slider will have outer dimensions to adapt the position of the buttons to.
Edit – I suppose the images will get a
z-index assigned as some point, otherwise the first image doesn’t even need any positioning at all.