RESTR AREA ENTERED WHILE AVOIDING HAZARDOUS WX.

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OUR FLT WAS BOUND FOR TRAVERSE CITY; MI (TVC) FROM DETROIT. THERE WAS A LINE OF TSTMS WHICH EXTENDED FROM JUST OVER TVC ARPT SW IN A LINE DOWN THROUGH OKLAHOMA. WE DECIDED TO DEVIATE AROUND THE LINE TO THE N. WE MADE THE DEV DECISION JUST S OF HOUGHTON LAKE ON V133. WE TOOK BASICALLY A 360 DEG HDG AND DUE TO STRONG NW WINDS; WERE BLOWN FURTHER E. OUR CLRNC WAS PRESENT POS DIRECT TO GLR; CHARLEVOIX; THEN TVC. AT APPROX CRAYLING; MI; ATC ADVISED US OF R-4201 AN ACTIVE SURFACE TO FL230. THE STORMS CONTINUED TO PUSH E AND AS WE NEARED THE W EDGE OF R-4201A; THE CAPT MADE THE DECISION TO TURN AROUND. I WANTED TO MAKE A L TURN TOWARDS THE WX; BUT HE TOLD ME TO TURN R AND WE PENETRATED R-4201A. I FELT THE HEAVIEST PRECIPITATION WAS STILL 3-5 MI AWAY; BUT DUE TO THE FACT THAT WE HAD A COMPANY CHK AIRMAN IN THE JUMP SEAT; AND DUE TO THE CAPT'S SHORT TIME IN THE L SEAT; I BELIEVE A RUSHED DECISION WAS MADE. THE LIGHTNING; TURB; AND ICE WERE FACTORS WHICH PROBABLY AFFECTED THE IRRATIONAL DECISION. ALSO; THE CAPT WAS OUT OF THE COM LOOP BECAUSE HE WAS COMMUNICATING WITH OUR COMPANY DISPATCH CONCERNING THE WX WHILE I WAS FLYING AND COMMUNICATING WITH ATC. ONCE THE CAPT GOT OFF THE RADIO WITH DISPATCH; WE DECIDED TO DIVERT TO PELLSTON; MI. WE ADVISED ATC OF THE DEV AND PROCEEDED TO PLN.