Well, she seemed to accept the apology. If we can all just forget about it now that would be great.
Never got the impression that Sirius was insecure. Think there's more to it? Remus ever cheated? Or has Sirius ever cheated? Cheaters are usually very insecure. Doesn't sound like a healthy reaction, either way.
Point - it's not your fault he reacted like that. He's clearly got his own shit going on.