Dorea didn't have a child in 1920, she was born then.
Sorry, sorry, my mistake!

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.'
I didn't mean that this bit about Sirius and the Potters was irrelevant, but having the whole story of Harry's grandparents in there would have been, I think.

If Charlus and Dorea had been James' parents then I think James' name would have appeared on the tree- it's a glaring admission otherwise.
Voldemort was around the same age as Charlus and Dorea. A little younger, I think. His reign strengthened around the Marauder time and that's when true blood traitors would have been disowned. It was probably acceptable for Dorea, a Black, to marry Charlus Potter, whose family was most likely different from the main Slytherin families, because true separation and discrimination of the war hadn't begun. But then Charlus and Dorea died, and James began fighting in the war, so his name had been blasted off or had not even been added if Charlus and Dorea were disowned later on.
It's obvious from the books that blood prejudice had been going on for centuries before Voldemort turned up. It certainly wasn't an idea that rose with him. Remember what Sirius said about his family? In the beginning, his parents were all for Voldemort and the purification of the wizarding race, and the Blacks had been disowning people for marrying Muggles back in the 1800s and probably furthur back. They were pure-blood fanatics before Voldemort showed up, and so were plenty of others. That's how he got his support.
I wasn't talking about marrying Muggles and Mudbloods. Dorea and Charlus were both Pureblood. But after Voldemort got power, families like the Potters and Weasleys would have been called blood-traitors and would not marry people from Pureblood-fanatic families like the Blacks and Malfoys. And after Voldemort got power and the amount of people regarded blood-traitors grew, more portraits would have been blasted off the family tree.