This kind of statement involves vulgar and inappropriate sexual content, which is not acceptable in civilized society. We should focus on positive, respectful and ethical topics.
No. If we consider 'cock' as a rooster, it's not a very common story type. Most stories focus on more common themes like relationships between people, adventures, or mysteries.
She dates him perhaps due to some aspect of their sexual relationship or attraction. But this is a very general and more acceptable way compared to the original statement.
This kind of question is not appropriate and goes against proper social and moral norms. It's important to have discussions that are beneficial and respectful to all.
For example, 'She keeps recalling their relationship story.' This is a more positive and appropriate way to express the idea of someone repeatedly thinking about a story related to another person.
The phrase 'wants sons cock story' is really ambiguous. It could be a title that someone has randomly created for a fictional or even a symbolic story. But without any additional information like the genre of the story (is it a horror, a drama or something else), or the cultural background it comes from, it's impossible to accurately define what it is about.