I'll be burning some vacation myself, but because I wanted to get some work done not just to ride there ... now that I put it that way, I see the flaw in my attitude. If you want to do it then I say go for it. Whatever reason you chose to work more, it's nobody else's place to judge.

For the literal question, I agree with others that only the miles traveled from home to work and back are truly commuting, but any errand "on the way home" counts.