One challenge could be the public perception. The wizarding world may not be very accepting of Hermione raising Voldemort's daughter. There could be a lot of fear and suspicion. Another challenge is Delphini's own nature. Since she has Voldemort's blood, she might have some inborn dark tendencies that Hermione has to constantly fight against. Also, Hermione would have to deal with the memories and legacy of Voldemort that might be a part of Delphini's upbringing.
In fanfiction, Hermione raising Delphini could face the challenge of isolation. Her friends might not support her decision fully, which could lead to her being isolated from her usual social circle. Also, Delphini's education about her family history would be a tricky thing. Hermione would have to find a way to tell her about Voldemort without glorifying him or making her feel ashamed. Additionally, there could be legal issues in the wizarding world regarding the custody of Delphini. Hermione would need to navigate through the complex laws to ensure she can raise Delphini properly.
Hermione would surely face the challenge of Delphini's magical upbringing. Given Delphini's powerful lineage, her magic might be different from what Hermione is used to dealing with. Hermione would need to find a way to teach her control and responsibility. Moreover, Hermione might struggle with protecting Delphini from those who seek revenge on Voldemort's family. There could be dark wizards or witches who want to harm Delphini, and Hermione would have to be constantly on guard. And, Hermione's own emotional state might be a challenge. She has to balance her love for Delphini with the knowledge of who her father was.
One challenge Naruto might face is Gaara's past traumas. Gaara has been through a lot of pain and isolation, which has made him distrustful. It would be difficult for Naruto to break through those barriers and get Gaara to open up. Another challenge could be the political situation. Suna and Konoha have had their differences in the past, and some in Suna might not be happy with Naruto's influence on Gaara. Naruto would have to deal with any potential political unrest or opposition from those who don't trust Konoha.
They might face social challenges. In the wizarding world, there could be those who don't approve of their relationship or their decision to raise a child together. Also, financial challenges could arise. Even though they are heroes, they still need to provide for the child's needs, like education at Hogwarts which might have costs associated with it.
One challenge could be dealing with their different personalities. Each sibling might have their own desires and goals. For instance, one might be more interested in military matters while another in the arts. Rhaenyra would have to find a way to nurture all of them individually.
One challenge could be Naruto's impulsive nature. He often rushes into things without thinking, and Tsunade would have to find a way to rein him in. Another might be dealing with Naruto's fame. Since he is the Jinchuriki of the Nine - Tails, he has a lot of attention on him, and Tsunade would need to protect him from those who might want to use or harm him.
One challenge could be his own reputation. Since Fenrir is often seen as a dangerous werewolf, other characters might not trust him around Hermione, which could make it difficult for him to carry out his protection duties effectively.
Financial difficulties could also be a problem. Naruto might not be well - off initially, and raising a child requires money for things like food, clothes, and education. He would have to find ways to provide for his sister while still being a ninja. Also, there could be threats from Naruto's enemies who might try to target his sister to get to him.
One major challenge would be understanding the magical world. Tony Stark is a man of science, and magic operates on very different principles. He'd have to learn about spells, potions, and magical creatures. Another challenge could be dealing with the wizarding community. They have their own traditions and laws, and Stark might find it difficult to fit in or make sure Harry follows all the rules. Also, protecting Harry from magical threats might be tough for Stark as his technology might not always work against magic.
Hermione would also face the challenge of secrecy. If the wrong people found out, it could put her in danger. And she might have to constantly lie to her friends and family, which would be really hard for someone as honest as her. In some fanfictions, this internal struggle is really well - explored.
In the fanfiction, Kakashi might face the challenge of Naruto's insecurities. Naruto has always had a complex about being alone and not having a family. Kakashi would have to find ways to make Naruto feel secure and loved. Also, dealing with Naruto's powerful and sometimes uncontrollable chakra could be a problem. Kakashi would need to train Naruto to master his chakra properly without it overwhelming him.
One big challenge could be Snape's natural inclination towards the Dark Arts. Harry would have to constantly keep an eye on Snape and try to steer him away from that path. Also, Snape's personality is often prickly and guarded. Harry would need to break through those barriers to really connect with him. Another challenge might be the expectations of the wizarding community. People might not understand why Harry is raising Snape and could be suspicious or judgmental.