im applying now. this is where the frustration stems.
Unfortunately this is called life, and it is what it is. It's not always 'fair,' whether you agree with your PI or others who have chimed in here or not. What's done is done, and the ship has sailed.
Yes, it's a red flag to not have a LOR from the PI from a research experience if it's one that you are highlighting on your app as a big significant experience. If you had multiple other more important experiences and you could make it look like you just had too many more important LORs that this one just didn't make the cut, then no one will notice. It would look really weird to make a big point about how interested in research you are, or how much this research impacted you or whatever, and not have a LOR.
If this research experience is a major part of your experiences (as in without it, your app is not strong), then your options are kind of the following.
*Take a gap year or two to gain more experience. I was ink a sort of similar situation, where I did a whole summer of wildlife work and it was so great I took a semester off to do another 7 months. Well things crapped out, and I left after 5 months (it was more their problem than mine, but it still sucked). I could still get LORs from there, but I felt like this was supposed to be a big part of my apps and it fell flat and I didn't want that. So I committed 2 years to biomedical research at a research powerhouse institution to get a glowing LOR from an important person while also running a cat rescue to build leadership experience. Did I "waste 2 yrs"? Maybe. But applying when you're not ready with the idea that you can then move on wastes a lot of time too IMO. By the time you give up after holding out hope and waiting for rejections and look for something else to really bolster your app during the gap year, you've wasted a year. Other people may see it differently. I ended up with my pick of vet schools and the experience made me competitive with scholarships.
*Having a postdoc or another non-PI faculty researcher in the lab write a LOR for you if you have one rooting for you and thinks it's sad the PI won't write you one (this is a desperate move, but if you really need one from this particular lab...). I would avoid one from a grad student or lab manager... If everyone kind of agrees with your PI, and you're that one student everyone kind of shrugs and shakes their heads when they think of you, don't do it. Make sure to explain the situation and ask if they can honestly write you a great LOR. Do NOT beg because your mean PI refuses to do so and they should feel bad for you because you had extenuating circumstances.
*Dont make excuses, and don't say anything about not getting a LOR or talk about your PI. But incorporate that you were not able to do your best in school and that your research experience suffered and that you were not able to commit as you would have liked to because of extenuating circumstances with your family. Even here, write what you learned from it if you really did crumble from the experience, or if you were resilient and the noncommiyment to extracurriculars were because you were trying to still maintain your academics then highlight that as a strength. Family/life issues often become more common as you get older and many people in vet school are affected, so if you can, you don't want to just blame it as justification for doing poorly and do nothing else.