There is a new and better road from Hanoi to Cuc Phuong national park, it is not goes through Nho Quan town:

From Phu Ly, you take the road of highway No1 passing Gian Khau bridge then turn right to Bai Dinh Pagoda. Behide the parking of Bai Dinh is a big road that leading to Cuc Phuong national park. By taking this road, it is 2km further than if you take the road to Nho Quan but it is less traffic and you can avoid the 10km bad road from Nho Quan to the park.