I wouldn't send it at all. It's not going to be a good letter, and they told you as much. That they had a bad letter prepared for you sounds particularly unprofessional, and if it were me, I would probably take it personally...because it is, when you consider what you have to do to put together a medical school application that gets to the point where LORs matter.
The LOR is a demonstration of institutional signals and not any true candid evaluation of your performance. The reality is that you're an undergraduate research assistant doing grunt work for free, pushing along what is presumably someone else's project. It's basically not showing up for volunteering because someone died. There's something so sinister about that, like adding insult to injury.
I mean, a strong letter is understood as one that leans so positive, it's saccharine. Everyone is in the top 5% of "all of the students [they] have ever trained." Hypothetically, if you have any negative quality, it's caring too much... (OK, this is a bit hyperbolic but I hope I'm conveying what I mean.)
To write anything that would call into question (or even give the appearance of questioning) an unflinchingly positive evaluation is not just "writing a balanced evaluation," it's a kiss of death.
There was another student here recently who received their letter from a nurse manager that tanked their cycle because they were very self-righteous about "writing the truth." That was completely out of pocket, but forgivable given that nurses generally don't know the subtext of medical school admissions... but a professor?! Straight to jail!
In the future, whenever you ask anyone for a strong letter of recommendation and they do not answer with "of course, I would love to write you a strong letter," do not take it! Anybody having to qualify and hedge their impression of you to your face is very likely not interested in seeing you move on to whatever it is you are applying for.
This individual is not the nice person doing you a favor that you think they are...and I'm sorry you had to witness a death in the family and return to academics bereft and completely unsupported by the mentors who should be encouraging and uplifting you. This is kinda messed up.
