I had the same problem on a DELL Latitude E5470 (Older model) that my organization redeploys as a spare when needed. I'm still trying to find a way to fix this in my deployments, but here's a fix I discovered:
After connecting a external Mouse and Keyboard;
- Open Device Manager
- Expand "Mice and other pointing devices"
- Right click on Dell Touchpad
- Click "Update Driver"
- click "Browse my computer for Driver Software"
- click "Let me pick from a list of available drivers on my computer"
- Choose "PS/2 Compatible Mouse"
- Hit "Next," reboot, and gesture to your heart's content
I even somehow got the ALPS control panel working, but that's more work for minimal payoff.