C172 Flight Instructor reported their student overshot the instrument approach course and descended below glidepath in IMC requiring the instructor to take control of aircraft and recover.

Narrative

My instrument student was flying. He had successfully completed two RNAV approaches at ZZZ1. We were returning home to ZZZ at 4000 feet under radar vectors with ZZZ Approach. Approach turned us toward ZZZZZ and issued approach clearance 'Maintain 3000 until established cleared RNAV runway XX'. We commenced descending to 3000. We were very close and he overshot the approach course. While trying to correct to course he lost focus and continued the descent. We were half scale deflected left and 400 feet low when I took over the controls. ATC issued an altitude warning I replied 'correcting' ATC said we were still right of the approach course I replied '3000 correcting. I descended to 2800 feet as we were then inside ZZZZZ; intercepted the approach course and turned the aircraft back to my student. ATC turned us over to tower. The ceiling was about 2200 feet MSL so we broke out shortly and landed.I was giving my student directions to get us back on the approach. He was not responding correctly. I waited to long to take command.