Confounding due to population substructure is always a concern in genetic association studies. Although methods have been proposed to adjust for population stratification in the context of common variation, it is unclear how well these approaches will work when interrogating rare variation. Family-based association tests can be constructed that are robust to population stratification. For example, when considering a quantitative trait, a linear model can be used that decomposes genetic effects into between- and within-family components and a test of the within-family component is robust to population stratification. However, this within-family test ignores between-family information potentially leading to a loss of power. Here, we propose a family-based two-stage rare-variant test for quantitative traits. We first construct a weight for each variant within a gene, or other genetic unit, based on score tests of between-family effect parameters. These weights are then used to combine variants using score tests of within-family effect parameters. Because the between-family and within-family tests are orthogonal under the null hypothesis, this two-stage approach can increase power while still maintaining validity. Using simulation, we show that this two-stage test can significantly improve power while correctly maintaining type I error. We further show that the two-stage approach maintains the robustness to population stratification of the within-family test and we illustrate this using simulations reflecting samples composed of continental and closely related subpopulations.