To try to press the case out, insert the lightning connector into the socket, and hold the protective case gently and then gently press the Lightning cable into the Apple charger case socket (which should be accessible) and gently press the protruding and thicker part of the end of the Lightning connector further in and use that pressure to slowly extract the charger case from the protective case.
Do not angle or torque or twist the Lightning cable in the socket. Straight in pressure only, and gently.
Failing that, refrigerate the protective case and charger case, and see if the plastics involved contract differently.
Failing that, borrow a Dremel tool or equivalent, and very gently and exceedingly slowly slice partial-depth into the protective case, and weaken the protective case incrementally until it can be removed.
Do not slice into the Apple case.