A PA28 INSTRUCTOR WITH STUDENT; ON APCH TO SSF; DSNDED BELOW THE MDA AND LANDED.

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AFTER THE MISSED APCH; WE PROCEEDED TO OUR DEST. ENRTE; I WAS MONITORING APCH CTL; AND BECOMING QUITE CONCERNED. AIRLINERS WERE DETOURING AROUND LEVEL 2 AND 3 PRECIP AROUND THE AREA. LEVEL 2 WAS ON FINAL AT OUR ALTERNATE; AND AIRLINERS WERE RPTING LIGHT TO MODERATE CHOP. WINDSHEAR WAS RPTED AT 250 FT AT THE ALTERNATE AND VISIBILITY WAS RPTED AS 1 MI. OUR DEST WAS RPTED AS 300 FT AND 3 MI. LEVEL 2 PRECIP WAS RPTED BUILDING ON EITHER SIDE OF OUR RTE. AS WE NEARED OUR DEST; I REQUESTED VECTORS TO VOR FINAL SO AS TO EXPEDITE AND SIMPLIFY ARR AS MUCH AS POSSIBLE. AT THIS TIME; WE HAD SPENT NEARLY 2 HRS IN SOLID IMC; AND FATIGUE WAS STARTING TO BE A CONSIDERATION. THE APCH WAS NORMAL. BEFORE THE FAF; TWR SAID THEY WERE 300 FT AND 2 1/2 MI. ON ABOUT A 3-4 MI FINAL; THE STUDENT GOT ABOUT 60-80 FT BELOW MDA; TWR CALLED A LOW ALT WARNING; AND WE CLBED BACK UP. AT ABOUT 3 MI OUT; I TOOK THE ACFT; AS I WANTED TO GET US BACK ON COURSE (WE WERE ABOUT 3 DEGS L OF COURSE). I STARTED CORRECTING BACK; AND AT THIS TIME; RECOGNIZED LANDMARKS ON THE GND. I FLY REGULARLY OUT OF THIS FIELD. MY ATTN WAS NOW FOCUSED ON THE GND; LOOKING FOR THE RWY; MY AIRSPD; AND THE VOR COURSE. I PAID WAY TOO LITTLE ATTN TO THE ALT; AS I SAW THE GND AND FAMILIAR LANDMARKS BELOW AND IN FRONT OF ME. I FINALLY SAW THE LNDG RWY ABOUT 2 MI OUT; SET UP FINAL AND LANDED UNEVENTFULLY. ALTHOUGH I WASN'T CHKING ALT; I AM PRETTY SURE THAT I BUSTED MY MDA. ALTHOUGH I PROBABLY BUSTED MINIMUMS; I FEEL IT WAS APCHING AN EMER SIT. I FEEL OUR ALTERNATE WAS NO LONGER A VIABLE OPTION. DIFFICULTIES RPTED BY HVY JETS AND APCH CTL MADE IT A NON-PLAYER IN MY MIND. RETURNING TO THE FIELD WE HAD SHOT APCHS AT OR ANOTHER FIELD IN THE AREA WAS OUT DUE TO INCREASED ACTIVITY ENRTE; THE FATIGUE FACTOR; AND UNFORECAST DETERIORATING CONDITIONS IN THE AREA. I FELT RELATIVELY COMFORTABLE WITH MY DEP FIELD AS I HAVE FLOWN OUT OF THERE MANY TIMES. AS I RE-LIVE THIS INCIDENT; I CAN THINK OF NO SAFER ALTERNATIVES TO WHAT I DID. WX FORECASTS: I HAVE ALWAYS BEEN SKEPTICAL OF FORECASTS AND KEEP 2-3 BACK-UPS IN MIND. WX TRAINING IN FAA; IN MY OPINION; IS MISFOCUSED. HRS ARE SPENT ON THEORY; AIR MASSES; AND CHARTS THAT MOST PLTS WILL NEVER SEE. A MORE OPS ORIENTED APCH INCLUDING INCIDENTS SUCH AS MINE MIGHT TAKE WX TRAINING OUT OF THE THEORETICAL REALM AND GET IT INTO THE REAL WORLD WHERE PLTS FLY. THANK YOU FOR THE OPPORTUNITY TO RPT THIS INCIDENT. I HOPE OTHERS MAY LEARN FROM IT.