I've been wondering too about how come Edmund doesn't fit the family pattern.

A newborn child isn't formless clay to be shaped as the parents desire - siblings can differ greatly from one another right from day one. So I'd assume there must be some genetic and 'in utero' influences at play which help make Edmund different from his siblings.

I picture young Edmund as an innately serious and obedient child to whom the behaviours approved of by Sir Thomas came more naturally than to his brother Tom. This would gain his father's approval which would encourage him to develop further in the direction Sir Thomas desired.

I see quite a few similarities between Edmund and his father. They are both rather conventional, restrained yet essentially good-hearted people. Both have a keen sense of duty. Both are intelligent and thoughtful but notably lacking in 'wit'. Neither has the extreme selfishness which is so evident in Lady B, Mrs N and in Edmund's siblings, though Sir Thomas does like to have things his way, and I wouldn't be surprised if Edmund became somewhat similar. Both men have somewhat fixed opinions. I haven't detected much evidence of flexibility in Edmund's mindset, and if he and Mary were to marry then I think Mary would be the one to be adjusting all her ideas to suit his rather than the reverse, even when there wasn't a moral component at issue. Even Edmund's attraction to Mary is not unlike Sir Thomas, who in his youth was "captivated" by Miss Maria Ward.

Empathy is a quality which Edmund possesses but seems entirely absent in the rest of his family. Why this should be I don't know. Perhaps it's innate, or maybe Edmund internalised some of the teachings in the New Testament more than any of the others?
We see Edmund's empathy most clearly when he befriends Fanny when she first arrives. There are occasions though, such as when Fanny is threatened with going to live with Mrs Norris, when what he has decided is the rational view seems to over-ride his instictive empathy.