Cessna 172 Instructor Pilot reported difficulty controlling the aircraft on short final when a regional aircraft's jet blast upset the aircraft.

Narrative

I was in a Cessna 172P model with a certificated pilot on a familiarization flight.We had departed the Wilmington airport and had been maneuvering in the Carolina Beach practice area. I asked my student to call in to Approach and request to come back in for some pattern work. We had been in the traffic pattern for two touch and go's and were instructed to fly left traffic for Runway 6. On the downwind; I called Tower and let them know I intended to do a go around/low approach for this next pass; Tower acknowledged my call. There was a Cirrus flying an instrument approach on short final; and a regional jet an unknown distance out; talking to the Tower as well. After the Cirrus had passed by us; the Tower cleared us to turn base for Runway 6. My student configured for the descent; and began his base turn. As we continued on our base leg; the Tower called for us to 'cross final; and join the right downwind for Runway 6. My student and I were confused by the call and asked for clarification. After some back and forth; my student and I realized that the Controller wanted us to make a right turn and fly an extended right downwind for Runway 6. He made a climbing right turn; with flaps in; causing us to slow down quickly. I instructed him to lower the nose; add power; and retract his flaps so that we would stop our descent and get back to a more suitable altitude for an extended downwind. Upon joining the extended downwind for Runway 6; the Controller told us to follow the regional jet passing off to our left. I looked over to make visual contact and noticed that we appeared below the regional jet we were to follow. At this time I had concerns about wake turbulence so I advised my student to climb to get above the regional jet's path before turning a right base for Runway 6. The student corrected our altitude and began a base turn. We turned final for Runway 6 and the regional jet had landed and was clearing the runway. At this time we were about a mile to a mile and a half final; still intending on the go around/low approach that we had advised the Tower we intended to practice. The Tower cleared a second regional jet for takeoff; right in front of us. My student and I discussed the proximity and worried; again; about wake turbulence. We always teach our students that wake turbulence is caused by an aircraft that is producing lift; and to 'stay in the bowl' to avoid a larger aircraft's wake. In an attempt to stay clear of the departing regional jet's path; we requested a full stop landing and were approved. The jet began its roll uncomfortably close; and I debated a go around but worried the side step would put us in an even more dangerous position so we slowed the aircraft down as much as we could to buy ourselves time and try to get to the runway threshold for Runway 6. The last 20-25 ft. over the runway; we experienced incredible turbulence and had difficulty controlling the aircraft; effectively wrestling it onto the runway. We both realized that we were so close that we flew into the residual jet blast from the departing regional jet that had been cleared while we were short final.