I had everything between the ESP8266 and the Arduino working in last post, but when I powered off the system and then restarted, nothing was working.
After a lot of head scratching, I found it was due to some ESP8266 boot up issue when the UART pins are tied to the Arduino. If I disconnect the UART pins between the Arduino and the ESP8266 and power cycle the ESP8266, everything works great. I suspect that the Arduino is holding the pins high while the ESP8266 is power up and it doesn’t like it. I will have to find a way to hold those pins low while powering up the ESP8266 somehow…. for another post.
After adding a level shifter to between the ESP8266 and Arduino, the ESP8266 doesn’t have problems booting any more.