Due to a quirk with Saiyan/Human half-breeds combined with a one-in-a-billion chance, Pan is Half-Saiyan.As You Know, you get half of your DNA from your mother and half from your father. So, there is a small, minute chance that the lucky sperm (which has half of the father's DNA, just like the egg has half of the mother's) had only the DNA passed down by Goku to Gohan. However, this would still prevent her from being half-Saiyan, due to the fact that an X would have to come from both parents. However, we do not know much about Saiyan DNA, or how it interacts with human DNA. We do know that a Saiyan immersed in Saiyan DNA heals faster, which means it doesn't follow human biology. So, perhaps due to a quirk with Sayian DNA, the sperm has both gender chromosomes (having two copies of the same X for females), and actually modifies the egg to remove the one that's there. Perhaps both her gender chromosomes are Gohan's X, which, following this weird quirk of biology (or, if you perfer, Ass Pull of mine) would also be Goku's X, which means she would be Half-Saiyan (and genetically, equally related to Goku and Gohan). Now, if her child (the mother or father of Goku Jr.) was fathered by Trunks (who likely died with seemingly every other Z Fighter), that kid would be half-Saiyan, so their child would be a quarter Saiyan, allowing Goku Jr. to go Super Saiyan. As for why Vegeta Jr.'s mother doesn't know Pan, perhaps the families (well, either Bra and Bulma or likely just Bra when it comes to the Briefs') had a falling out over the fact that she was the only fighter to not die, including Vegeta and Trunks.
Alternatively, something bad happened about ten years before the finale that caused a falling out between the Briefs family and the Son family.The fact that Pan is raising her grandson suggests something happened to Goku Jr.'s parents. This could be related to the reason why Vegeta Jr.'s mother (presumably Bra's daughter/granddaughter) doesn't recognize Pan. Something terrible happened that killed Goku Jr.'s parents, and the two families blamed each other for it and stopped speaking to each other. revealed outside the anime, Eis is the embodiment of the wish to remove the memories of Majin Buu. So, he's the living embodiment of about 6 billion mind rapes. So, physical rape seems pretty much within his character, seeing as that's the physical equivalent of mind rape.
Pan was an accident.Pan was 5 (or 4) about 5 years after the Buu Saga. This means that Videl had Pan while she herself was still a teen, perhaps still in high school. Something tells me that wasn't on purpose.
The entire series was all a dream.Because no WMG page is complete without this theory.
Emperor Pilaf is a Time LordSame reason as the above, and hey. It would explain his presence.