Is the sole Muslim father in the family considered the guardian of his daughter born out of wedlock, and is she entitled to choose her guardian if he is not?

Scholars have differed regarding the lineage of a child born out of wedlock. The majority of them hold that such a child is not attributed to the fornicator, even if he claims him, but rather only to his mother. Some scholars, however, are of the opinion that the child is attributed to the fornicator if he acknowledges him, especially if the mother was not married to anyone. This latter view is the more probable one, and it was chosen by Sheikh al-Islam Ibn Taymiyyah and his student Ibn al-Qayyim. They based their reasoning on sound analogy: if a child is attributed to his mother and inherits from her, even though she committed fornication with him, and the child was conceived from the coitus of the two fornicators and they both agree that he is their son, then there is no impediment to attributing him to the father if no one else claims him. Accordingly, your father would be your legal guardian.