I am curious whether it is possible to parent an object to two objects. Perhaps have a condition that if a mouse button is pressed the child is the parent of the “mother” and if the space bar is pressed it is the child of the “father”.
How would that look in a script? Can it work?
You can’t parent an object to two other objects at the same time. I can’t begin to imagine how that behaviour would work. 
What you can do is change the child’s Transform.parent property back and forth between the first and second parent, which sounds very much like the thing you want to accomplish.