My wife's first year of med school there was a teacher that constantly belittled students. She wrote gotcha questions in the exams (that weren't correct) and would do tests the day before she scheduled them to "keep you on your toes."

My wife was one of the few people passing, but that didn't stop her from helping to organize a walkout. They set up a table in front of the class, got two hundred signatures, and forced the dean to compel the teacher to take her meds. She was audited for the rest of the year and retired two years later.

Professors can be crazy. You're not going to provoke a walkout because, as you say, you're unique. Therefore you need to understand and diffuse the situation solo, which is a lot more challenging.

She seems to have her head wedged about respect. You showing up late is clearly disrespectful in her mind. This is why she confronted you in front of the entire class rather than ask you to stay after class. Once you called her on the fact that she fucked up, she couldn't back down because then she'd look foolish (yes she looks foolish anyway but foolish and proud beats foolish and cowed).

You need to go to her office hours, tell her you're late to her class because of scheduling conflicts entirely beyond your control, and as you're not at fault you'd appreciate it if she'd be an ally rather than an enemy. Then let her know that if she couldn't come to some resolution that will help you graduate, you'll take it up with the dean.

She'll lose. She knows she'll lose. You're giving her an opportunity to save face.

You don't have to like her. You don't have to like it. But with as much going on as you have, take the easy way out.