A rather interesting plot hook has presented itself, and has made me curious as to the relationship between Dhampir and their respective vampiric parent. I have looked into some of the basic information provided for each, but it does not speak too much on the relationship between the two.
Is there any existing lore that speaks about the relationships or disposition usually held between these two?
More specifically the Fullblood Moroi vampire towards their half-blood offspring?
From the Dhampir description, under Variant Dhampir Heritage Details, with emphasis:
Since their undead progenitors often deal with royalty, svetochers have a fair chance of being born into nobility. Though some aristocrats are content to raise their moroi-born children in the shadowy corners of high society, less scrupulous nobles have few qualms about leaving their disgraceful offspring on the doorsteps of unfortunate commoners. Moroi rarely care for their half-breed progeny any more than the nobles forced to bear them, but those who do feel a sense of possession over misbegotten children might seek them out in the village they were abandoned in.
Anything beyond this is up to the specific GM and player. Any specific Moroi may or may not care; it does not seem like they would be openly hostile unless the Dhampir in question is doing the ungrateful progeny thing and taken the Vampire Hunter alternate racial trait and/or the Kinslayer Inquisitor archetype.
For more information, Paizo clarifies in the Vampire Templates:
The standard vampire template creates what most people would consider a “common” vampire. They sometimes call themselves “moroi” to distinguish them from other kinds of vampires, which are inferior in their estimation.
For more information, look at 'classical' vampire literature like the eponymous Dracula (but not Nosferatu; he has his own Template). The obvious example is Count Alucard, the Son of Dracula (1943). In the original movie, he does not interact with his father, unfortunately. In the Castlevania series based on the same concept, he has dedicated himself to ending his father as a personal choice.
Ifusaso's answer is good, but I wanted to offer this additional example:
The fantasy book Pathfinder Tales: Bloodbound, published by Paizo details an adventure by a Dhampir working for her grandfather, who is a Vampire Lord in Ustalav, and her relationships with a number of her full-vampire relatives.
It wasn't the best Pathfinder Tales book (some of which are excellent) but I still enjoyed it. It was particularly useful for the insight it provided me into Dhampirs, but also into Undead (and Negative Energy) in general.
The following contains some spoilers based on my recollections of the book (which I read well over a year ago):
She was intentionally bred by the Vampires as a go-between and problem solver for the Vampires' interactions with Ustalav. The quote Ifusaso found "feel a sense of possession over [their] misbegotten children", accurately describes how her grandfather views her — though I don't recall him actually turning up in the story, while his power and influence is felt everywhere. Her full-vampire wastrel-seeming sibling, is one of the book's main characters and often acts like a devil on her shoulder — though their relationship is very, very much coloured by their mutual grandfather.
Both of her parents turn up later in the book, though they were both previously unknown to her. Her father — being an older vampire — is fairly obsessed with maintaining a status quo that is in the process of spiralling outside his control (Positive energy is creativity; and Vampires are powered by Negative Energy - change is increasingly unpleasant to them). And as such seeks to manipulate her into restoring that status quo, but this is mostly driven by his feeling that she as his progeny should serve his goals.
