I agree with LIS....either cut out a lot of filler or elect to forego using the statement altogether. Even if it's just to save you characters, I don't know that it's necessarily to walk the reader through each individual step in your undergraduate career. The adcoms can already see what schools you attended, what jobs you've held, etc. For example, you could consider paring down your 3rd paragraph to something as simple as "Due to my dedication that is seen in my many responsibilities, I was able to transfer to Cornell." Or whatever. I'm not even sure why you would discuss your Cornell transfer. Remember that you are using this statement to discuss only any issues, red flags, etc. that may be on your application. You also contradict yourself by saying you are working on your ADHD with a provider, but later say you've got it managed.
I think it might help the content along if you briefly describe why you took time off in 2014. I worry that schools might read all of this and think "Well, is she going to drop out if she loses a family member in school? Can she handle family matters while in school?" It may sound a little heartless, but schools want students that give them reasonable confidence that they will finish out the program. Life does not pause because you are in vet school. Some schools give students a really hard time when it comes to family stuff popping up during exams or clinics, depending on what it is. I think you need to find a way to phrase certain things so that it's less "I experienced a loss, so I had to stop going to school briefly." I'm not sure what that phrasing would be (another reason to consider leaving this statement out altogether), but just think on it. This is only my opinion, so if you want to leave it as is, by all means do so. Everyone handles grief differently, just make sure you're not leaving any worries in the reader's mind.
Overall, it doesn't seem to have any direction. Again like LIS said, you don't really specify what you're explaining, you kind of just word vomited your hardships into an essay. Sometimes not talking at all is better than talking too much, and I really do think that may be the case for you. Like you said, your grades were never terrible, and you've managed to get some work experience under your belt too. Taking 6 years to finish undergrad isn't a red flag IMO since many non-traditional applicants are in the same boat. I think you could probably go either way with writing an essay vs. not at all, but make sure any version you do go with is the best it can possibly be.
B's are not grades to be ashamed of, at all. It's just that the average vet school applicant hangs out around a 3.5. This shouldn't prevent you from applying, you just need to apply strategically and kick butt in as many non-academic categories as you can. Watch out for the GPA cutoffs, compare yourself to previous classes, and so on. There are a lot of ways to find the best schools for you. It helps to be in communication with the schools as well, as the buck stops with them. You can certainly ask them if taking longer than the traditional four years is a concern, or if they feel you need to explain mostly B's. Some schools are more open than others. I got my best feedback during file reviews and was pretty frustrated in the answers I got before I applied, but it's worth a shot.