Fellows, let me ask you about the procedure of switching controllers during OTA.
My sensors are connected to a serial gateway, which is operated by a controller.
In my case the controller is Domoticz server hosted by Raspberry Pi2.

So if I want to initiate updating one of my nodes over the air then I need to... stop my current controller on my Raspberry Pi2 and... start a new gateway on a Windows machine with MYSControler, wait when all nodes will re-discover the new gateway and connect, and then use MYSControler to do all updates I need?

Right, I can of course switch the relay pin directly in the loop() just after the push button was pressed.
There will be no magic, meanwhile I am looking for a graceful scenario when everything works perfectly

Well, now I understand that the node based on RelayWithButtonActuator.ino will only change the state after pressing the button when the ACK is received back from the controller...

I this case I think I found a bug because I checked in MYSController and saw messages sent from my node/gateway like that 0;1;1;0;2;1

It sends always value 1 because never receives ACK feedbacks from the controller, which should cause toggling the value.
And It never receives ACK feedbacks from the controller because it actually doesn't request ACK - we can see fourth zero meaning no ACK required! And it should be different because ACK request is hardcoded in the RelayWithButtonActuator.ino :

send(msg.set(state?false:true), true); // Send new state and request ack back