PIPER PA28 INSTRUCTOR PLT ENTERED IMC DURING STUDENT TRAINING IN PRACTICE LNDGS AND THEN SUBSEQUENTLY CROSSED A PARALLEL RWY WITHOUT CLRNC DURING TAXI IN.

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ATIS AT PAE WAS CALLING THE CEILING AT 1500 FT OVCST. TOOK OFF WITH MY STUDENT TO DO LNDGS; STAYING IN THE PATTERN. AS WE TOOK OFF THERE WAS A LOWER SCUD LAYER APCHING FROM THE S. ON THE 2ND TKOF IT LOOKED LIKE THE LAYER WAS APCHING PRETTY FAST. ON THE 3RD TKOF WE HAD TO TURN AN EARLY XWIND TO AVOID ENTERING THE CLOUDS. COMPLETED A FULL STOP LNDG. I SHOULD HAVE DISCONTINUED THE LESSON AFTER THE 1ST TKOF SINCE IT ALREADY LOOKED LIKE THE MARINE LAYER WAS RAPIDLY APCHING. FELT LIKE I HAD TO FLY BECAUSE MY STUDENT HASN'T FLOWN IN A MONTH. AFTER LNDG WE WERE XING RWY 16L AT PAE I SAW AN ACFT FLY OVERHEAD. I TOLD MY STUDENT TO CROSS SINCE GND HAD CLRED US TO OUR PARKING AREA AFTER EXITING RWY 16R. THAT WAS PROBABLY AT LEAST 5 MINS PRIOR TO US XING RWY 16L. (IT WAS A LONG TAXI.) I'M QUITE SURE THAT WE WERE CLRED ALL THE WAY TO OUR PARKING AREA. IT WAS QUITE EARLY AND THAT IS A COMMON CLRNC WHEN ARPT TFC IS LIGHT. I'M HOPING WE DIDN'T GET AND MISS AN AMENDED CLRNC TO HOLD SHORT OR THAT I MISCONSTRUED THE ORIGINAL CLRNC. I WAS TALKING TO MY STUDENT; DISCUSSING THE LNDGS HE JUST DID. AT THE VERY LEAST I SHOULD HAVE CONFIRMED WITH GND THAT WE WERE CLRED TO CROSS.