Authorship dispute on a paper that came out of a final report of a course?
While it's impossible to judge contribution from outside, I generally recommend erring on the side of inclusion when it comes to authorship. If there's a reasonable argument that somebody contributed, it doesn't really cost you anything to have them on the paper.
Furthermore, there are many ways to contribute to a paper (see, for example, the CRediT taxonomy), and many journals even require a contributions section in which you can explain who exactly did what. In this case, it sounds like you wrote the paper, designed the system, built the system, and both of you ran experiments. You can't ethically "undo" somebody's experimental work by redoing it yourself.
What you should never do is to drop somebody from authorship without consulting them. You had a draft with this person on it as an author, and even if they never got back to you, for all they know they're still a co-author. Probably it doesn't matter to them very much (or else they'd likely have gotten back to you), but it's still unethical to remove somebody from authorship without their consent. It is also unethical to submit a paper without the consent of all of the authors, so that's also a potential problem in this situation, where you're just kinda doing what you feel like without consulting with anybody else.
In fact, the basic problem I see here is that you seem to be operating without any advice from somebody who can help you navigate these questions (as well as the issue of quality, which I won't touch otherwise). Your advisor is likely a good source of such advice, and even if you don't like/trust your advisor, you should be able to find somebody who knows the scientific world well who can be a mentor for you.
You have exactly two reasonable options here:
Withdraw the article, or
offer to your group mate to add her name to the paper. (She may decline of course - that is her decision to make, not yours and not your adviser’s).
I can’t say which of those two options are better for you, but in the absence of other information I would tend to assume that the adviser knows what they’re talking about when they say you should withdraw the paper.
In any case, your group mate participated in the creation of the results, so it is indisputable that she has a right to be a named author on the paper. The fact that you reproduced her results after the fact is irrelevant. The fact that you feel that you were coerced to work with her is also irrelevant, and remains irrelevant even if we all agree that you could have done everything just as well (or even better) without her. The only thing that would be relevant is if she is asked her opinion, given an offer free of any pressure to have her name added to the paper, and decides that she’s not interested and gives her approval for you to remain the sole author.
Finally, the one thing I find a bit puzzling in this story is that your professor’s requests are a bit self-contradictory: if they really thought the paper was so bad that leaving it online would hurt your reputation, I don’t quite understand why they think it would serve the interests of your group mate to have her name added to such a low quality paper. But that is neither here nor there, and doesn’t change the gist of what I wrote above about your options for handling the situation.
To answer your question shortly, if you have made a manuscript with her name on it and send it to her. Then yes you can't delete her name without giving her a deadline to come back with suggestions/corrections. And as jakebeal mentions, just because you do something again, does not equal that she never did anything. I can easy see that you are very angry in this matter, so I'll give you my suggestion. She should be given a "chance" with a deadline to return with a contribution to the manuscript. In any case, she should be mentioned in the contribution for performing experiments. And lastly, stating that the advice given from your advisor is not interesting to you, is foolish as people (usually) get professorship for a reason and advice should be cherished and not thrown. IMO