B737 Undifferentiated or Other Model
Flight Crew Last 90 Days 105; Flight Crew Type 4391
Situational Awareness
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Airspace Structure; Weather; Procedure
We had multiple small to medium size thunderstorms in the area departing LAS and encountered frequent light to moderate turbulence during our climb.  We were able to avoid most of the strong radar returns.  As we passed BTY we advised ATC that we needed to deviate West around weather ahead.  ATC advised us that if we could go North then we would avoid weather near OAL as well and would be clear past OAL.  We had just enough time to turn North and still avoid the weather.  I was insuring the Flight Attendants were still seated. I noticed that the First Officer was turning closer to the weather. When I realized that ATC had requested that the flight turn towards the weather I advised that we would be unable to do so. When told by ATC that there was a restricted area ahead; I [used captain's] and told ATC that we would not fly any further west and to contact the airspace authority for said restricted area.
B737 Captain reports being unable to comply with ATC instructions to avoid restricted airspace while deviating around thunderstorms and tells ATC to inform the restricted airspace controlling authority of his presence.