Dorea didn't have a child in 1920, she was born then. If you think she's James' mother, then we're talking about 1960 and 40 was a normal age to have children It's not the 1860's, and dying at 57 is by no means elderly, unless you're living in the middle ages.
Dorea was 57. So she was born in 1920. Don't think about the world now, but the world of 1920. I think, according to people in that time, forty would have been an extremely long time. Didn't people used to have children not long after marriage, in their twenties? If you're writing a fic in the historical or marauder time period, age forty being "late" for a child would probably be acceptable.
Read the scene from the book again, rather than remembering the film.
It was mentioned earlier that Sirius didn't mention to Harry who his grandparents were and what they were like. In the family tree scene in OotP, Sirius was talking about his past. Harry's grandparents are dead and irrelevant to the story. Either JKR was focused on telling Sirius's story, which mattered, or deliberately left out Harry's grandparents.
-OOTP page 103/104 Bloomsbury edition.
'You ran away from home?'
'When I was about sixteen,' said Sirius. 'I'd had enough.'
'Where did you go?' asked Harry, staring at him.
'Your dad's place,' said Sirius. 'Your grandparents were really good about it; they sort of adopted me as a second son. Yeah, I camped out at your dad's in the school holidays, and when I was seventeen I got a place of my own. My Uncle Alphard had left me a decent bit of gold - he's been wiped off here, that's probably why - anyway, after that I looked after myself. I was always welcome at Mr and Mrs Potter's for Sunday lunch, though.'
Jo Rowling did have Sirius mentioning Harry's grandparents and they're very relevant because that really builds the bond between Harry and Sirius and shows exactly how much Sirius longs to have Harry in his life. This is exactly the moment when he would say, 'Oh, and look, Harry, we're related.' Molly isn't so far off the mark when she accuses Sirius of thinking Harry is James. That speech above illustrates the tie between Sirius and James. I would still stand by putting Mr and Mrs Potters' deaths after the Marauders left school - so past 1978, but before 1981.
Regarding the blood prejudice. As Sarah said, it did not begin with Voldemort. For one thing, what was Grindelwald fighting for, then? And why were so many Black family members behind things like Muggle Hunting. Why would Isla have been blasted off the tree if Muggleborn prejudice didn't exist.