"Popping in" unexpectedly is bad enough, turning up at someone's home when they've SPECIFICALLY told you it's an inconvenient time is plain rude!
Don't worry about offending her she clearly doesn't give a stuff about your feelings or needs or your family's!
As pp say there's really no excuse in this day and age to not check if it's convenient first AND if told it's not just don't bloody turn up!
There's also no rule that says you HAVE to admit people who turn up like this!
If she does that again say
"It's really not a good time, I did say so when you called/messaged, I'll get in touch to arrange another time/I'll see you on X day, have a good day bye!"
NO apology, no long explanations.
Personally I don't even answer the door unless I'm expecting a visitor.
"I also think in this day and age , being aware re mental health and being supportive" many of us who DON'T like "poppers in" have mental health issues that mean people "popping in" causes us anxiety and distress - or does that aspect of mental illness not matter?
People who don't mind "poppers in" seem to be very presumptuous in expecting everyone else to feel the same!
Newsflash! People are different!