Welcome aboard.:wave:
Click on the button, then click on the spline point you want to split. now you can move the points apart.
You can only split points of the correct type that match the button from the section you are in, the track window button will only split a track point and the spline objects section button will only split spline object points (roads and fences and so on).
Hope that helps.

Just got pipped to it by you Dave.