Jaime x Lyanna Child Alternate Story Fic

How would Jon's life be more harsher if he is the Son of both Lyanna and Jaime?

But he's a knight who broke an Oath from being a Kingsguard, while Lyanna Stark ranaway and broke a betrothal between house Stark & Baratheon. Which these two had started a whole rebellion and caused so many deaths.

Man this kid's life would've been very traumatized and has a way more harsher life than Canon Jon.

But who's gonna look after the kid?

Would it still be Ned? Or would it be Tywin?

And who's also gonna love this alternate Jon? I know that Tyrion would love him since he is the son of his brother Jaime, and also Ned Stark since he's also a his Sister's Son.

And who's also gonna hate the kid? It's probably Cersei and Robert would truly hated Jon. Because he is the product of their lovers whom rejected and betrayed them.