Anytune ignores the value of the Play/Pause Control Command received, since Play/Pause is a toggle of current to opposite state. That is strange behaviour.
Please ensure your sender and Anytune are configured to be sending on the same single channel. Sometimes when set to all channels 16 messages are sent resulting in 8 cycles and nothing to have happened. I cannot explain why it would required two clicks unless your remote control is sending one command and then a completely different command.
You could also try the learn feature and see if it is always learning the same command.