Parent Object to two objects at the same time during animation


I have got problems concerning the animation of one object being parented to two objects at same time during an animation. I guess I would need child of constraints, but if I apply 100% influence to both constraints, the child object changes its position and if i click “Set inverse” it still does not go where it originaly should belong to…so can anyone help me out?

I am not sure if you are using armatures; just mesh objects, or a combination of both.

Would you please clarify, as each type has specific requirements.