The conflict might be more subtle. Ginny could make passive - aggressive comments about the child, which Harry picks up on. He tries to talk to her about it, but she denies any ill feelings. As time goes on, the tension builds until it finally explodes in a big confrontation where all the pent - up feelings are let out.
It could be portrayed as a cold war. Ginny might give Harry the silent treatment when he takes the child's side. Harry, on the other hand, might start spending more time away from home with the child, leading to a growing distance between him and Ginny. This could also affect their relationship with friends and family, as others start to take sides.
The conflict could be shown through arguments. For instance, Harry defends their child's actions or beliefs that Ginny doesn't approve of. They could have shouting matches in their home, with the child witnessing and being affected by it.