One major challenge is likely to be their own insecurities. Hermione might be insecure about whether she can be a good mother while still being an active part of the wizarding community in terms of her intelligence and contributions. Draco, on the other hand, might be insecure about living up to his family's name and expectations while also being a loving and present father. And then there's the whole aspect of combining their magical skills and knowledge to protect and educate their future child. There are so many different spells and potions they need to consider for the child's safety and development, and they need to make sure they're on the same page about which ones to use.
Well, they could face challenges related to their past. They were on opposite sides during the war, and that could create some underlying tensions. Hermione might worry that Draco's old prejudices could resurface, and Draco might be concerned that Hermione will hold his past against him when it comes to raising their child. Additionally, there's the matter of family support. Hermione's Muggle parents may have a hard time understanding the wizarding world aspects of raising a magical child, and Draco's family might not be fully on board either.