CRJ-200 FLT CREW HAS A TRACK HDG DEV AND TCAS RA WHILE ON THE 'EXPRESSWAY VISUAL' TO RWY 31 LGA.

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AFTER REVIEWING THE LGA ATIS THAT FO HAD WRITTEN DOWN ON TKOF/LNDG DATA SHEET I BRIEFED A VISUAL APCH TO RWY 31 BACKED UP BY THE LOC 31; WHICH WAS SET IN THE VOR NAV AND FMS. NO COMMENTS OR CORRECTIONS BY THE FO. AFTER SOME VECTORING LGA APCH CLRED US DIRECT TO DIALS INTXN. THE DIALS FIX WAS NOT LISTED ON THE FMS LEGS PAGE. I HAD APCH CTL SPELL IT. I ESTIMATE IT WAS ABOUT THIS TIME THAT I HEARD AN ACFT AHEAD OF US BEING CLRED FOR THE EXPRESSWAY VISUAL. A 'DING DING' WENT OFF IN MY HEAD. THAT'S THE APCH AFTER ALL THE INST APCHS IN APCH BOOK. I SCRAMBLED TO GET THE CHART OUT. FO HAD GOTTEN DIALS ENTERED BUT WAS UNABLE TO GET A MAGENTA COLORED 'TO' PRESENTATION ON FMS PAGE. IT SHOWED BLUE; I FIGURED WE'D PASSED THE FIX. APCH ASKED WHERE WE WERE GOING. I SAID WE'RE HAVING TROUBLE WITH THE DIALS FIX. 'DON'T YOU HAVE A CHART OUT?' 'NOW I DO.' I THINK APCH GAVE US TURNS TO 030 DEGS AND 070 DEGS AND ASKED IF WE HAD THE FREEWAY. AFTER SOME UNCERTAINTY LOOKING AT THE SEA OF LIGHTS THAT NYC PRESENTS I DID PICK OUT THE FREEWAY. FO THEN POINTED OUT THE ARPT TO THE L. I SAID FIELD IN SIGHT; WE COULD DO A VISUAL TO RWY 31. AS I REMEMBER; WE WERE CLRED FOR A VISUAL TO RWY 31. I TURNED R TO ENTER A DOWNWIND; NEEDING SPACE TO GET DOWN. WHILE TURNING TO BASE; APCH ORDERED AN IMMEDIATE L TURN TO 030 DEGS (?) WHICH WAS CONFUSING SINCE I WAS ALREADY TURNING L. WHILE IN THE L TURN I WAS TOLD 'TURN R IMMEDIATELY TO 130 DEGS (?); TURN R IMMEDIATELY.' THE TCAS WAS SHOWING A RED RA. BACK TO WINGS LEVEL; I WAS UNABLE TO RE-ENGAGE THE AUTOPLT IN 3 ATTEMPTS. IT WANTED TO DSND. I TOLD THE FO TO DIAL IN 332 (LG NDB) IN ADF TO HELP RE-ESTABLISH OUR POS. SOME TIME LATER SHE HADN'T DONE IT SO I DID IT MYSELF FEELING VERY MUCH IN NEED OF ORIENTING MYSELF. FIRST KNOWN POS AFTER INTERRUPTED BASE TURN WAS APPROX LGA 220 DEGS 11 DME. CONTINUING TO FOLLOW VECTORS; WE EVENTUALLY CALLED RWY 4 IN SIGHT AND WERE DOING A VISUAL WHEN TOLD TO GO AROUND; WHICH WE DID. NO EXPLANATION. MORE VECTORS FOLLOWED BY AN ILS TO RWY 4 AND AN UNEVENTFUL LNDG. ONCE PARKED I CALLED LGA TRACON MGR AS INSTRUCTED. HE WANTED TO KNOW WHERE I WAS GOING UP THERE. HE ADVISED THAT NEW YORK AIRSPACE HAD BEEN SHUT DOWN; PLANES PUT INTO HOLDING AND 3 OTHER AIRPLANES ALMOST SMACKED. I EXPLAINED ABOUT TURNING R TO ENTER A DOWNWIND; ABOUT THERE BEING NOTHING ON THE ATIS ABOUT THE EXPRESSWAY VISUAL; ABOUT HOW THE FIRST TIME I HEARD ABOUT IT WAS FROM THE AIRPLANE AHEAD OF US. UPON RETURN TO ACFT I HAD THE FO PULL UP THE ATIS. ATIS INFO SHOWED 'EXPRESSWAY VISUAL 31.' I ASKED FO HOW COME SHE DIDN'T WRITE IT DOWN. SHE SAID EXPRESSWAY VISUAL WAS ON THE BOTTOM LINE OF ONE PAGE OF THE ACARS SCREEN AND '31' ON FIRST LINE OF THE NEXT SCREEN. SHE JUST MISSED IT! I DON'T RECALL IF ACARS SCREEN ACTUALLY READ 'EXPRESSWAY VISUAL 31' OR 'EXP VIS' OR SOMETHING ELSE. I HAVE WHAT SHE COPIED THE SECOND TIME. THE FIRST TIME SHE ONLY WROTE '31' AND DID NOT ADVISE OR QUESTION ME WHEN I BRIEFED A VISUAL TO 31 BACKED UP BY A LOC 31 APCH. THIS WAS MY SECOND FLT TO LGA IN 14 YRS; THE FIRST BEING THE WK PRIOR WHEN AN ILS 22 WAS PERFORMED WITHOUT INCIDENT. FO HAD BEEN ONCE BEFORE; LAST FALL SHE BELIEVES. ADDING THE EXPRESSWAY VISUAL TO SIMULATOR TRAINING MIGHT BE GOOD. IT SURE HELPED INTRODUCE ME TO SOME OF THE HAZARDS/PERILS OF THE LGA VISUAL APCHS.