Modeling human behavior is essential to accurately predict epidemic spread, with behaviors like vaccine hesitancy complicating control efforts. While epidemic spread is often treated as a simple contagion, vaccine uptake may follow complex contagion dynamics, where individuals' decisions depend on multiple social contacts. Recently, the concept of complex contagion has received strong theoretical underpinnings thanks to the generalization of spreading phenomena from pairwise to higher-order interactions. Although several potential applications have been suggested, examples of complex contagions motivated by real data remain scarce. Surveys on COVID-19 vaccine hesitancy in the US suggest that vaccination attitudes may indeed depend on the vaccination status of social peers, aligning with complex contagion principles. In this work, we examine the interactions between epidemic spread, vaccination, and vaccine uptake attitudes under complex contagion. Using the SIR model with a dynamic, threshold-based vaccination campaign, we simulate scenarios on an age-structured multilayer network informed by US contact data. Our results offer insights into the role of social dynamics in shaping vaccination behavior and epidemic outcomes.