Arduino Due with ESP8266 simple AT command

I have an Arduino DUE and want to connect it to an ESP8266 Board and then test the connection with a simple "AT" command on the serial command line. I have written a lot on the internet but there are so many different answers on this topic and none of them solves my issue directly.

I set up the eps8266 correctly with the two power cables. They are even comming from different power sources, so there should not be a problem with the power for the esp board.

I think the problems are somewhere in the different baud rates. If I choose 9600 Baud for the connection from the Arduino to the PC via USB and 74880 for the connection from the esp board to the DUE I at least get the error messages correctly when the esp board has to restart (when I force it).

ets Jan 8 2013,rst cause:1, boot mode:(3,6)

load 0x40100000, len 1396, room 16
tail 4 chksum 0x89 load 0x3ffe8000, len 776, room 4
tail 4 chksum 0xe8 load 0x3ffe8308, len 540, room 4
tail 8 chksum 0xc0 csum 0xc0

2nd boot version : 1.4(b1)
SPI Speed : 40MHz
SPI Mod
le:52mn

The code is the following:

//always high
int CH_PD_8266 = 53;

void setup() {
  Serial.begin(9600);
  Serial3.begin(74880); //--> at least error code is shwon correctly

//  Serial3.begin(115200); //error code is gibberish
  pinMode(CH_PD_8266, OUTPUT);
  digitalWrite(CH_PD_8266, HIGH);
}

void loop() {
  while (Serial.available() > 0) {
    char a = Serial.read();
    Serial3.write(a);

    //Write back to see if it even comes perfect
    //Serial.write(a);
  }

}

void serialEvent3() {
  while (Serial3.available() > 0) {
    char a = Serial3.read();
   // Serial.write('A');
    Serial.write(a);
  }
}

Any help would be really appreciated.

I had to do a workaround, described in this question:

Why do I need to change the Baudrate after I send a Reset to the ESP8266?

Also the ESP is very sensitive to currency changes. Sometimes it needs a little push by injection a little voltage from the outside (via voltmeter....). After I do this the communication starts.