C680 First Officer reported a loss of aircraft control and momentary stick shaker during arrival in weather conditions.

Narrative

The initial phases of flight all was ok barring a few minor issues with radios and figuring out things out it being the first time flying this jet or any jet for that matter. Upon starting the descent we went into some moderate turbulence and heavy precipitation and were being vectored down onto an approach. I had loaded the FMS slightly incorrectly by activating vectors to final rather than the entire approach which may have decreased the situational awareness of the pilot flying and I did not correct the mistake in a timely manner and being relatively inexperienced in the plane I did not realize or remember from training not to load the approach in this manner. However we got down to an altitude of about 3000 successfully and then were continuing to get heading vectors. I answered the radio for the new heading change while the PIC attempted to change the heading but instead grabbed the altitude knob and began scrolling it to a lower altitude thinking he was manipulating the heading bug. I noticed the incorrect altitude change and then we got an ATC advisory of an altitude alert and were told to correct. The PIC then over corrected for an altitude loss of around 1000 by adding full power. At this point the autopilot was disengaged. From the over correction I then mentioned we were climbing excessively; the PIC then over-corrected again and reduced the throttles to or near idle without adjusting pitch enough. I then noticed our airspeed was quickly dropping off and then we were approaching a stall with an excessively low airspeed. At this point I believe I felt the stick shaker; and the pilot flying verbally announced a stall and attempted a recovery which I ultimately felt I needed to assist in the very uncomfortable situation and help him to regain control of the aircraft which we did around 9000 feet and then proceeded inbound on the approach again. After recovering the PIC continued to hand fly back in through consistent moderate or greater turbulence causing further altitude deviations.I think the primary cause of this was the lack of experience in the crew on top of less than ideal weather. With more experience flying I would have loaded the approach correctly allowing for more situational awareness and with more experience the PIC may not have manipulated the wrong control and could have recovered more efficiently with less deviation in airspeed altitude and heading and power changes for the initial altitude loss keeping the aircraft in better control through the mistake.To prevent this situation from occurring again more experience before going into weather could have been beneficial. More proficiency in the systems and SOPs for the PIC and SIC for the plane I feel could have mitigated or lessened the difficulties in recovery from the initial problem of altitude loss.