Hi Spike,
That’s certainly a weird issue.
It might be worth checking the touchpad settings - some touchpads have a feature to disable the keyboard when typing, it might be disabling the touchpad altogether with the keyboard connected
Easiest way to find the settings is to press Windows + R, type ‘control mouse’ without quotes into the run box and click OK. There will possibly be a Synaptics or ELAN tab here, or underneath the Hardware tab there will be additional options.