Delay in mouse movement when using both the keyboard & mouse simultaneously

On touchpads made by Synaptics, this is a "user-comfort" feature called PalmCheck. Touchpad operation is intentionally blocked when you are pressing keys on built-in keyboard.

You can disable the feature in control panel "Mouse" by minimizing PalmCheck sensitivity. Open mouse control panel and follow yellow highlights from top to bottom:

When changing the 'delay' setting to "No Delay (always on)" does not work, go to regedit and follow this registry path:

HKEY_CURRENT_USER>Software>Microsoft>Windows>CurrentVersion>PrecisionTouchPad

Then change "AAPThreshold" from 2 (or, whatever value is set) to 0.

You may have to reboot for changes to take effect.

The behavior may also be down to the drivers; so if the above did not work, ensure that they are up to date. Driver updates are usually found in Windows Update, Optional updates section.