Why Would Dany Worry When Jon Is Even A Threat Anyway & Would Likely Need Her To Confirm His Parentage To Be Recognized As Rhaegar's Son Who - Tumblr Posts

I just … really dislike the idea that Dany would view Jon as a threat in nothing more. Daenerys - especially in the books - longs for nothing more than home and a family, and will cling to anything and anyone who gives her a sense of belonging. Every other family member she had is dead - father, mother, brothers (she even mourns Viserys!), husbands, Rhaego - and her recurring thoughts of them and the house with the red door point to her real priorities. It’s why she forms bonds so quickly and sometimes doesn’t pick up on hints that someone shouldn’t be trusted, like Jorah’s betrayal or (in the books) Brown Ben Plumm’s fake-care and eventual turn. It’s also why she refuses to turn away the refugees from Yunkai that decide to follow her, even though it’s detrimental both to them and her own forces (none of them are soldiers, they only have what they can carry, and Dany doesn’t have enough food to feed them all). She considers them her children, and can’t turn them away. This is most obvious with regards to Drogon, Rhaegal, and Viserion. She’s their mother, and she believes they’re the only real children she’ll ever have, so she is completely devoted to them. 

If/when Dany finds out that Jon is a Targaryen in the books, any “threat” he posed would be a secondary concern to her in comparison to her joy at actually having a living family member (… well, if he stops being dead).