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 $\langle p,p\rangle_{1,0}$, the number of lines through two points.
issoroloap
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