Transferring Twice-Advice on a "good reason" to do so

In 2013 I attended Occidental College, I was there for a year before I decided to transfer to a different school. I took a gap year and applied to BC and Oberlin, both of which I got into. I chose to go to Oberlin and have been there for two months, but due to family issues (my mother was in poor health and it has recently relapsed, she lives alone) I feel compelled to continue college closer to home. BC is in the same town that my mom lives in, in addition, I personally would prefer to go to school there because of it’s location, history program, and more lively social scene. My question is this: What should I write in my transfer essay? Do I just make note of the primary issue, which is my mothers health, do I give a list? What should be kept out?

Be honest.
As you write you will find there are certain things that you want to emphasize and others you realize are relatively trivial.
Admissions doesn’t want to hear anything but the truth, and they are certainly well equipped to read between the lines if you’re trying to hide your reasons (you have good ones btw).

that makes sense, I think my main worry was conveying the personal reasons (i.e. my mother’s health), while also emphasizing my desire to attend BC for it’s history program, and for being a good school in general, I don’t want the admissions officers thinking my only reasons are circumstantial

Honesty works best. Your mother’s health issues seem to be the primary reason for wanting to transfer and BC is the school that best fits you needs both geographically and academically.