WiFi problem on Mega + WiFi R3 ATmega2560 + ESP8266
I had this problem. On Robotdyn D1 mini the esp8266 flash erase did help. On Robotdyn D1 R2 only the flashing of the AT firmware with Espressif Flash Download Tool restored the esp8266. After then the sketches from IDE had working WiFi.

There are some settings of the Espressif basic esp8266 libraries (SDK) saved on flash and there is some incompatibility between SDK versions. The Flash Download Tool creates right esp settings binary and flashes it to right address on flash.