This whole bloody movie never makes any sense. Because Marty wouldn't remember his now changed childhood because he never lived it, but his brother and sister lived it and they'd have memories of Marty living it with them growing up. They grew up well off with a successful father, would have had a whole different upbringing, memories, vacations etc. Basically Marty would have to act like he woke up with total amnesia and remembers nothing of his whole life. But this new reality Marty still ended up with the same GF? Their relationship would be totally different in this new reality as well.
So if his father knew his future some was a time traveller the father wouldn't know what his life was before Marty changed it. He would have lived his life normally post-Marty and become successful writer. And if Marty was born and raised in that environment he very likely would have never met Doc Brown, and thus wouldn't have time travelled in the new reality.
Time travel like this can't happen.
As opposed to the way it
does happen? Second by second, into the
fyootchah?!
One way to reconcile the time-travel dilemma is to accept that time-travel is one element of the one single timeline. That there is no reality where Marty doesn't go back in time, and hence there is no what-if speculation otherwise. He
always went back in time and everything
always happened where events are wholly re-written (and none negated). The father is BOTH a failed and successful writer; the family is both poor and rich; etc. etc.
In this: the father doesn't connect the dots, but the mother has an inkling.
Their knowledge is a result of their character quirks. George McFly is a dreamer deep inside his own head, as is wont of many writers. Lorraine is more of the salt-of-the-earth 50s type whose field of knowledge hinges on the banal, so any weirdness beyond what a 1950s girl would readily accept is simply ignored. But she does give Marty a look of familiarity, which definitely tips it off. But, like I said, a 1950s girl would think such an idea would be "fiddlesticks."
There have been movies that address how it is someone posseses knowledge of "both" timelines. Usually it's the agent of change who retains memory, having lived out the first timeline and being aware of the change. Sometimes it'll be the case where the initial memories fade under the weight of the "new" memories. My personal philosophy is that whomever is closest to the change, and the bigger part they play in said change, the more they will be aware of the change. The further down the chain of responsibility, the less the inkling. But this doesn't apply to BACK TO THE FUTURE. None but Marty and Doc and Biff are aware. (Marty's girlfriend, too.)