He'd be frantic. Tony loves his daughter deeply, so he'd immediately start searching for her. He'd use all his resources, his technology, and his connections to find her.
At first, he might be angry, thinking she's being irresponsible. But then, as he realizes the possible reasons for her running away, he'd be filled with guilt. He'd blame himself for not being there for her enough. He'd probably stop at nothing to get her back, and when he does find her, he'd be very emotional. He'd hug her tightly and promise to be a better father, to listen to her more and give her more space if that's what she needs.
Tony would be in a state of shock. His daughter is his world, and her running away would be like his worst nightmare coming true. He'd likely go into a bit of a self - destructive mode at first, blaming himself for every little thing he might have done wrong. Then, he'd pull himself together and start a very methodical search. He'd enlist the help of the Avengers, his friends like Pepper, and anyone else he could think of. He'd be constantly worried about her safety and well - being until she's back home.
He would be extremely worried. Tony Stark, despite his tough exterior, loves his daughter deeply. He'd probably start by using all his resources to find her. He has access to advanced technology, so he'd likely use his Stark Industries gadgets to track her down.
He would probably be overprotective at first. Tony has been through a lot, and the idea of his daughter having mutant powers, which could make her a target, would be scary for him. He might try to keep her locked away in the Stark Tower, but that would likely lead to her rebelling.
He'd probably be shocked at first. Tony is always so caught up in his own world that a secret daughter would be a huge surprise. But then he'd likely be protective. He might try to keep her away from his dangerous life at first, but as he gets to know her, he'd start to include her in things.
Well, she might run away because she feels overshadowed by her father's fame. Everyone always talks about Tony Stark, Iron Man, and she may feel like she's just an afterthought. Maybe she wants to find her own identity away from the Stark name.
Tony would also likely expose her to the world of science and engineering from a young age. He might take her to his lab and let her play with non - dangerous parts while he works. This would help her develop an interest in those fields.
Tony would probably be extremely hurt. He trusted his team, and betrayal would cut deep. He might initially be in denial, not wanting to believe that his friends could turn on him.
The Avengers would be in a state of panic and fury. Captain America would likely lead the charge to find Tony. He'd use his military strategy skills to plan a rescue mission. Thor might use his godly powers to track down any signs of Tony's whereabouts. Black Widow and Hawkeye would be on the lookout for any Hydra agents or informants. Hulk could be a wildcard. He might be uncontrollably angry and ready to smash anything in his path to get to Tony.
Steve Rogers would probably be deeply disappointed. He values loyalty highly, and Tony's betrayal would shatter the trust they had. He would try to find out the reasons behind it and might even try to bring Tony back to the right path if he thought there was a chance.
Tony would be a protective father. He'd raise the child in an environment full of knowledge. He'd introduce the child to his friends like Pepper, Rhodey, and the Avengers. The child would grow up hearing stories of heroism and would be inspired to be a good person. Tony would also use his wealth to give the child the best education possible, but also let the child explore their own interests. For example, if the child showed an interest in art, Tony would support that as well as their scientific pursuits.
In some fanfictions, their relationship could be a bit rocky at first. Maybe the adopted daughter has a different view on how to use technology for good. But through various events and heart - to - heart conversations, they grow closer and learn from each other, with Tony learning to be more open - minded and the daughter learning the value of his experience.