I'll start with a couple of quotes from Ibn Ishaq, Biographer of Muhammad:
He had people put to death for mocking him ('Asma' bint Marwan, Abu Afak, Ka'b ibn al-Ashraf, Khalid ibn Sufyan, the list goes on).
He had more than four wives at one time (his revelations only allowed 4 wives max. he had up to 11)
He had sex with a nine year old.
He smashed all the Pagans' idols.
In terms of the historical Muhammed, rather than the theological Muhammed, it is very difficult to know much about his actual life.
He is generally considered to be born in the 'year of the elephant' (the elephant story itself lacks historicity), however according to various sources he was born 15 years before that, or 3 or 10 or 15 or 20 or 23 or 30 or 40 or 50 or 70 years later (
Source). If something as straightforward as this produces such a range of opinions, it seems very strange that much of the rest of his life is described in minute detail.
The sirah has him existing in an overwhelmingly pagan environment, whereas the audience for the Quran is clearly scripturally literate else much of it wouldn't make sense (There are actually numerous mistakes made in exegesis as some of the medieval exegetes were not aware of the intertextuality with Christian/Jewish teachings).
Even something like Aisha's age at marriage is uncertain. She was a divisive figure from a sectarian perspective, with questions raised by her detractors about her chastity. Having her marry at the age of 6 could simply be an attempt to preclude any possibility that she wasn't a virgin when she was married (especially given her previous betrothal). Or the sirah might be accurate, it's ultimately unknowable though.
It is a work of theology written 100+ years after the fact in a totally different environment, rather than a work of history recording events with regard to their historicity.
I know for the purpose of your discussion it's not really important, what matters is what people believe he did. It's worth pointing out though. If more people realised many things likely didn't happen, it would be easier to negate certain lines of extremist argument that relies on brutal events from the tradition.