How to cross major road 3 way intersection
Options in order of preference: 


Another route. 
Stop on the south side, wait for straight though (north/south) traffic to stop, choose your time to cross contending only with single right turn lane out of PonyExpress Parkway. (Turning traffic is slower, minimizes damage if you get hit). If you don't make it all the way across before lights change, you are in the left turn lane for the next phase. 
Be assertive and use the left turn lane but only if its a cycling friendly town. problem with this move is at 50MPH, if it goes wrong, it goes badly wrong. 


Also Lobby local authority to make it safer. They have gone to expense installing cycle lanes, so they should at least give you a fair hearing.