I find this question particularly intriguing. Taking into consideration the (little) material there is to base a theory on, here are my thoughts on that subject:
Mummy Holmes - as we learn in HLV - is a genious herself. And while her husband doesn't seem to be a genious, I guess we can savely assme that he's not stupid either. So them having three genious children is not that unlikely to begin with. Mummy seems to have strong genes, after all.
In the short family video we saw at the beginning of TFP Sherlock and Mycroft didn't seem sociopath-like at all. Sherlock seemed to be a happy, affectionate child playing around on the beach, at some point playfully hugging his elder brother. Mycroft on the other hand seemed a bit of a loner, but not sociopath-like either. He seemed to enjoy the attention he got from his brother, as we can see in the video and by the little smile on grown-up Mycroft's face when he watched the video. I can imagine that Mycroft being seven years older than Sherlock, being the nerdy and slightly overweight "know it all" kid in school, had a very hard time making friends (kids can be very cruel to kids that are different) and thus mostly kept to himself, learning early on what it means to be lonely. But being a bit of a loner didn't make him a sociopath back then.
I think Eurus, on the other hand, actually was a psychopath. But she's the only one of the three. I think that Sherlock and Mycroft were deeply scarred by what happend with Victor and everything that followed his disappearing and Eurus burning down their house. Sherlock must have been desparate, after all he was just a six year old boy who had just lost his best friend. And I can imagine that Mycroft, seening his little brother suffer so much over the loss of his best friend, actually convinced himself that he was much better off having no friend at all.
We don't know how quickly Sherlock started to rewrite his memories after Eurus was taken away, and we also don't know why his parents let him do so, but maybe partly forgetting the horrible things that had happened to him was the only thing that made him better. Maybe he even was sick for some time, forgot most of the events and just remembered "Redbeard". And to spare him pain, his parents (and Mycroft) told him that Redbeard had been their dog. I guess we'll never know the details. But I guess from then on Sherlock subconsciously started to distance himself from others more and more ("alone is what protects me"), following his brother's example of avoiding pain by keeping away from anything he might regret losing.
And from then on, I can also imagine Mycroft being quite a bit of a mother hen (M: "I'll be mother" - S: "And there's our whole childhood in a nutshell" ASiB), constantly making sure Sherlock would focus on his rational side, constantly challenging him and pushing him to do the best he can, but without getting emotionally attached.
So to sum this - far too long - post up: I don't think it was the Holmes partent's upbringing that made Sherlock and Mycroft into the want-to-be sociopaths they claim to be (but clearly aren't). I think if it hadn't been for Eurus and the events mentioned in TFP, Sherlock would probably still be a very warm and charming person, maybe even a bit of a womanzier. Mycroft on the other hand would probably still be a bit of a loner, but more open to the notion of friendship and maybe even love.