skipping the awfulness part for a moment, consider getting AAA or a similar car service that you can call for emergencies like this.
now as for how your AH reacted? abusive bluff and bluster, that is all. he is seizing upon you making a single mistake in order to try and justify the heaps and mounds of mistakes he has made and continues to make.
make this the last time you cater to him whatsoever. no more rides, no more dropping the kiddo off to make it easier for HIM. and if he dares raise his voice to you again, you immediately remove yourself - or hang up - or open the damn car door and push him out onto the street. ok, maybe NOT the last one.
you are not a bad mom. NOT A BAD MOM. do not take ONE word of what comes out of his mouth as god's truth. see it like verbal vomit, and step around it.