I have pretty much the same problem as in Dell XPS 13 9350 with Ubuntu 15.10 - Touchpad freezing, jumping - but on Ubuntu 16.04.
My touchpad stops working randomly, or can work somewhat only if I click and drag with it. Sometimes it starts working if I do a two-finger scroll, but this doesn't always work.
I have installed a mainline kernel (version 4.4.13-040413-generic) to fix an issue related to resuming after suspend. However, the present touchpad issue was present on a vanilla 16.04 install too.
Any help is appreciated. How would I even begin debugging this? (I am not shy to use the terminal or modify my system, as long as I know how to bring it back to a working version, in case the experiment fails).