I think keeping it with the original "how to deal with the difficult parts..." form makes the question either unclear or too broad, since there's so much out there that can be construed as "difficult". Anti-Islam websites such as the one linked in the post make a point of making things look as difficult to accept as possible, because that's in their best interest.
But they don't always use the same techniques. Sometimes they'll present questionable evidences as if they're authentic, sometimes they'll ignore piles of evidence and only use the single piece that supports their argument, sometimes they'll just twist words around to meet their needs, sometimes they'll just present seventh century Arabian mores through the filter of twenty-first century American ideals.
And sometimes things are just difficult to accept because you don't know all the details involved in the issue (the tale of Al-Khidr in the Qur'an being a prime example).
As I see it, there's two forms that this question can take to be constructive, depending on what the questioner himself actually wants:
- Focussing on the specific situation (i.e. the killing of Umm Qirfa), where it becomes objectively answerable either by tearing down the arguments made by the linked website, or providing authentic evidences in a more neutral manner to clarify the actual incident.
- Focussing on how to deal with anti-Muslim rhetoric in general, which isn't so much about dealing with "difficult parts" (as the original title and example would imply) as it is about critical reading on the whole.
Given the comments made by the questioner, I suspect the second form is more likely what he's actually seeking an answer for at this point.