You asked a question, and after thinking about it, I have a carefully-considered answer. You were both wrong. Your husband innocently (but nonetheless not correctly) started to change what I assume was a messy diaper in public. For many reasons, that is not a good idea, some of which you may not have considered. Aside from the unsanitary conditions (at least on the changing tables in the restroom, only babies are being placed), someone could have snapped a photo of your husband and baby (undiapered), and sent it into cyberspace. While I am sure some people are groaning now that I thought of this, it has happened before.
Sometimes you have an emergency and the public is the only place, but please consider that not all people enjoy the sight of a baby being cleaned up and changed. Some people even get nauseous at the sight (and odor). We love our babies and don’t think twice about it, but you wouldn’t want people to watch your toddler using the bathroom in public, your baby should not be treated differently.
The woman was WAY out of line, especially if she was using unsuitable language. But once you saw she was clearly in need of anger control, you should not have further engaged with her. What you said ( I am sorry to say) to her was also out of line, though I DO understand what prompted you to say it. Honestly, I would have picked up and moved to a different area after that and not spoken to her at all.
I might have said (if anything), “You’re right – I’m sorry that we offended you; have a nice day,” and would have moved on. That would have shocked her, and shut her up.