I didn't read all the replies, so I'm mostly just replying to the original post. The fact that he asked her for change before his second visit and expressed resentment for it not occuring the previous time, she should've felt ashamed that she forgot to bring it up then, and pay extra attention to this next time he came, but instead of apologizing that she did it again, she had the guts to suggest that he should pay a higher rate by default. She totally deserves to lose this customer for this behaviour. It happened to me a few times that I didn't have change, I told them, they said it's okay, they probably intended to tip anyway because it often happens. Naturally the envelop thing is a clearcut way to say that what's in it is mine, but I prefer notes in hand because I count it regardless, no cover to slow me down without it. I don't like being prude about doublechecking for various reasons, like it happened that they gave less by accident, we confirmed the extra charges this way, or they upgraded from what we previously agreed on.
Don't wait to get confident. Just do it, and eventually the confidence will follow