As Dan says, you can use the divisor equation:
$$\langle e_{\alpha_1}, \ldots, e_{\alpha_n}, \ell  \rangle_{g,d} = d\  \langle e_{\alpha_1}, \ldots, e_{\alpha_n} \rangle_{g,d} $$
where the $e_{\alpha_i}$ are any cohomology classes of $\mathbb{CP}^2$, to reduce your invariant $\langle p,p,\ell \rangle_{0,1}$ to $\langle p,p\rangle_{0,1}$, the number of lines through two points.