What are the subsequent inputs to the DES key schedule after round 1?
As you already correctly observed, to get $k_1$, you rotate $C_0$ and $D_0$ left to obtain $C_1$ and $D_1$ and apply PC-2 to $C_1$ and $D_1$. 

To get $k_2$, you simply rotate $C_1$ and $D_1$ left to obtain $C_2$ and $D_2$ and apply PC-2. To get $k_3$, you rotate $C_2$ and $D_2$ left to obtain $C_3$ and $D_3$ and apply PC-2. This continues until $k_{16}$. Also see Figure 3 in the Wikipedia article on DES for a graphical illustration. The round keys $k_1, \dots, k_{16}$ are then used in the round function of the respective round.