Translation:Besides me she also remembers my brother.
So I'm guessing since this uses "min" in the accusative, the idea is that she doesn't just remember me, but she also remembers my brother... right? And if it were meant as not just me remembering my brother, but also she remembering him, it would be "mi", right?
The alternative is that "krom" just goes with the accusative, and that doesn't seem to be in the spirit of Esperanto.
Your last interpretation is correct: "She remembers me in addition to remembering my brother." "Krom" normally includes, its excluding meaning (except) is better covered by "escepte de".
Example: "Ĉiuj krom mi" = All except me.
"Krom mi, ankaŭ ĉiuj aliaj ..." = Additional to me, also everybody else ...
I wrote a report, so they will describe it more clearly.