After almost 5 years of searching for the answer, I think you could be refering to American Eagle 230 at Chicago O'Hare, which happend on december 27, 2000. The aircraft was an Embraer 135.
I could not find the video, but here is evidence it once existed.
The Wayback Machine does seems to have a copy of it, but since it is an .exe executable in a zip file, I am not touching it even with a long stick.
The aircraft was pitching up steeply due to trim problems, and to get the aircraft to descent, the pilot used steep banks ('50 or 60 degrees'). They also executed a 360° turn to get lower for landing. I could see how this may have felt analogous to the Space Shuttle, which involves flying S-turns and then a 270° turn to align with the runway.
The NTSB report with Incident Number CHI01IA055 says:
The captain said that during takeoff from O'Hare International Airport (ORD) the airplane
accelerated normally, rotated, and "jumped into the air". At 800 feet agl, the captain called for
the climb checklist. It was about this time that the captain noticed that he could not trim nose
down. The captain had the first officer check his trim switch and the backup system. They did
not respond. The captain elected to bring the airplane back to ORD. The captain said that both
he and the first officer had their control yokes pushed forward to the stop and were still
climbing. The captain said he was finally able to stop the climb and level the airplane at
approximately 8,000 feet. The captain said they declared an emergency and referred to the
Pitch Trim 1 and 2 Failure checklists. The checklist directed they lower flaps to 9 degrees.
"When we brought in the flaps, the aircraft pitched way nose high. We were out of control."
The captain regained control of the airplane and had the first officer retract the flaps. The
captain said they lowered the landing gear. It improved the airplane's stability slightly. They
pulled and reset the trim circuit breakers twice. These actions did nothing. The captain said he
lined up for an approach to runway 9R. The captain determined he was too high to land, so he
executed a 360-degree descending turn. On completion of the turn, the captain said they
needed to slow down so they deployed the spoilers. The captain said the airplane abruptly
pitched way up. The captain said he and the first officer pushed both yokes forward. The
captain advanced the throttles, and retracted the spoilers. "That second, I banked hard left, 50
to 60 degrees as I recall, and chopped the power. It took all our abilities to get the nose down."
After they got the airplane back under control, the captain said approach control informed
them that runway 4R was straight ahead. The captain elected to land on runway 4R. The
captain said he left the airplane configured as it was (landing gear down, flaps and spoilers
retracted) and flew a long shallow approach. "I said to myself, God please let me land this
airplane. Over the runway, I chopped the power and let it settle on the runway." A postincident examination of the airplane's spoiler control unit revealed that when the spoilers were
given the command to retract, the unit was not sending an input to the horizontal stab control
unit (HSCU) to put in 1 unit of nose down stabilizer trim. Examinations of the trim system
components and the other airplane systems revealed no anomalies. Following the incident, the
airplane's manufacturer revealed that the horizontal stab actuator was determined to be
inadequate to move the horizontal stabilizer in all flight conditions. "The incidents are most
likely caused when the flight crew fails to trim the airplane after takeoff before reaching a
certain airspeed where the air loads on the stabilizer may overpower the trim actuator,
resulting in the horizontal stabilizer not responding to the pitch trim command from the flight
crew." The manufacturer issued an alert service bulletin mandating the installation of a
cockpit placard and revisions to the airplane flight manual establishing a maximum speed of
160 knots to pitch-trim after takeoff. The FAA issued an emergency AD mandating the
installation of the cockpit placard and revisions to the airplane flight manual. The FAA has
also tasked the manufacturer to make design changes that will enable the trim actuator to
handle increased load limits. The FAA has also mandated changes that will provide improved
pitch trim failure indications and ergonomic improvements of the yoke trim switches.