Integrated correlators with a Wilson line in a $\mathcal{N}=2$ quiver gauge theory at strong coupling

We consider the four-dimensional $\mathcal{N}=2$ quiver gauge theory arising from a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills with gauge group $SU(2N)$. We study the integrated correlator between a half-BPS Wilson line and two Higgs branch operators of conformal dimension 2. Using supersymmetric localization, we resum the perturbative series for this observable and obtain exact expressions for both the planar and next-to-planar terms of its large $N$ expansion, valid for arbitrary values of the 't Hooft coupling. Finally, through a combination of analytical and numerical methods, we determine the leading terms of the corresponding strong-coupling expansions.