Not sure why you are trying to configure a mail server to relay mail through other mail servers...just use an email client (Thunderbird, Evolution, etc.)
That said, the error message is pretty clear:
Code:
SASL LOGIN authentication failed: authentication failure
You are apparently not properly authenticating to the relay server.
Also wondering about
Code:
relayhost = [my.relay.domain]:26
It would be very unusual for a relay server to be listening on port 26...
PS. If you want to persist with configuring postfix, you'll need help from someone else...I don't speak postfix.