I can only assume you are married to this person because he is your cash cow and you are a SAHM.
To answer your question: fuck no, DH would never, ever make me do drop-off if I was feverish/sick and it was on his way. Double fuck no if it were on the way to a recreational event vs. work.
But then, I'm in an equal marriage and don't have to be a slave to someone else to justify my existence/get decent treatment. I suggest you look into it.
Wow. I mean, I agree with you and everything. (I'm a PP DH.) And I like the way you express yourself. But, project much?