Is History of Chassidus part of Jewish Life and Learning or is it too specific?
It depends on the scope of the question. If your question is something like:
then it seems within scope. If your question is something like: "What are all of the concepts put forth by the Chassidim which the Misngadim found wrong, and what did the Misnagdim do what the Chassidim thought wrong, and what did they respond to each other", well, one can write a book about that.