Are you really sure that your my_mapping.object() point to your object for which you try to call the Click() method ? As you explain your problem it seem that you object support the click() method but your my_mapping.object() not, so we can assume that maybe your mapping properties for this object can return several objects or to another object and that when you call the click() method, the method is called on a different object that doesn't support the method.
To validate this theory, you can try to highlight your control from the mappedName file and see what TC return to you.
