Caroline is the Wizard's daughter with the Witch. The Witch was pregnant when she left him and didn't tell him because she didn't want to have to see him after he broke her trust. He suspects this, but can't know for sure without talking to his ex, which he's clearly afraid to do. Hence why he thinks he has a daughter in town but isn't certain.
When Caroline says Pierre gets jealous, she's referring to the world of magic that she's a part of but that he can't touch. He was afraid early on that she would leave to explore her magical heritage. So she started sneaking to the Wizard's tower to see him and/or her mother (via the portal) and not telling Pierre. He could tell she was being sus and that's what led to him wondering if she was having an affair and if Abagail was truly his child. She is, the family just has all kinds of communication issues.
Robin used the Dark Shrine of Memory on her ex-husband after she and Demetrius got married because Demetrius is possessive (like how he is with Maru). She did not tell Sebastian about it, so he has no idea why his dad suddenly went no-contact when he was a toddler.
Clara likewise used the DSoM on Alex's father. After getting diagnosed with a terminal illness, she knew she couldn't leave Alex alone with him. Neither her parents nor Alex know this is why the abusive jerk finally left.
