I'm not sure if this is of any help but can you disable "tapping" ?
I used to use a Dell laptop 4 years ago, belonging to my employer. What happened to you was also happening to me, and I used a wireless mouse every time I was able to, ie when I was sitting at a desk. But someone showed me how to disable the tapping feature of the mousepad. this allows you to operate the pad by tapping, rather than drawing your fingertip across, or using the buttons. Once that was switched off, things were much easier.