ESP 12E resets on connecting to a client in WiFi mode
My guess is a power supply problem. An active ESP8266 uses much more current (~ 300mA) than other components you might have worked with.

That 'you robot' power supply uses SMD linear regulators to reduce your 12V to 5V and 3.3V. When you draw 300mA from the 5V with an input of 12V (is it really 12V or somehwat more??) the 5V regulator dissipates 2.1W, which is way too much.

For a test, my can try a beefy USB power supply (at least 1A).

If this solves the poblem, I suggest you use a switching mode PSU to reduce the 12V to 5V and 3.3V.