Lesley Hazelton's book is basically a paraphrasing of the story found in Islamic sources and so isn't at all useful for the OP, in addition to not being written by a historian of this period. As for Tom Holland, his book is a fun read but his views are not the academic consensus right now (see my critique of his views/TV series here) - a better starting point would be Robert Hoyland's new book, In God's Path. It is also written for a popular audience, but Hoyland is easily one of the most influential historians of early Islam today, unlike Holland, who has never written a serious history book.

If the OP is looking for alternative viewpoints, James Howard-Johnston's Witnesses to a World Crisis contains a decent re-examination of the Battle of Karbala - he placed the battle within the First Fitna, with Ali's two sons fighting on after his death (based on a analysis of the Chronicle of Theophilus of Edessa. I can't think of any other Western historians who have specifically looked at the battle itself (military history is not exactly in fashion right now, so the focus is on social/cultural history, or to reinterpret the traditional narrative of the Arab Conquests as a whole). Still, I recommend Howard-Johnston's book whole-heartedly. It's a pretty academic book and so is quite difficult to read for an outsider, but his analysis of the sources is really top-notch and I think his revisionist narrative is very convincing.

You can read about this battle in this book:

After the Prophet: The Epic Story of the Shia-Sunni Split in Islam by Lesley Hazleton

Tom Holland's In the Shadow of the Sword might point you in the right direction. It's popular history about the origins of Islam, and would be an ok place to start.