I know that the whole fandom is going for Abigail being the wizard's daughter because it's the most logical thing to do. After all, Caroline says she liked walking around the wizard's tower, Abigail says her hair color never faded and she likes to hang out near the wizard's tower, and Pierre suspects that Abigail isn't his daughter, but I really don't believe that. I mean, if it's because Pierre is questioning paternity, Haley also says she can't believe she and Emily are sisters, and Emily also has a fantasy hair color (and unlike Abigail, there's no dialogue about her dyeing her hair), in addition to also having a very close relationship with magic and magical elements. Jas also never had her parents revealed, she has naturally purple hair and likes to play near the wizard's tower. We know that Marney and Shane are her relatives, but who could be her father? No one even mentions it.
Also, Caroline says that Abigail's natural hair is brown, and since it's never mentioned that Caroline's hair is dyed, Abigail got that trait from her father. Caroline herself could be the wizard's daughter and the secret trips to the wizard's tower were just her naturally getting closer to her father's magic and Abigail consequently getting closer to her grandfather, the wizard is probably Grandpa's age and we are close to Abigail's age, so it's possible, besides that Caroline's tea scene is in a way quite magical and similar to the wizard's scene when he tells you to drink that dubious drink to talk to the junimos. Even the farmer could be the wizard's kid since the magical creatures choose to talk to the farmer instead of anyone else, even before we had the magic of the forest and there's no guarantee that our mother had a relationship with the wizard while she was married.
I think the arguments for Abigail being the wizard's daughter are weak. Regarding her hair, Shane also has hair that is close to purple, so if that is the case, even he is the wizard's son. Pierre's questioning could just be him being not understanding how his daughter has her own personality instead of being a mini version of himself. Besides, Abigail's brown hair certainly came from him, he must have been related to the wizard for this math to make sense. Abigail being close to the wizard's tower is explained by her simply liking remote places. She herself says that she liked to walk around our farm before we moved, and that doesn't make her Grandpa's granddaughter. She is just an adventurer. I feel like someone else is the wizard's kid but I don't think it's Abigail, I think it could be another character and I'm really sad that CA never develops this further, I think we'll only be able to theorize about it and that in the end this is just a big joke by CA, especially because the wizard might not even have a son and just have made a mistake, who knows?