Urban transport networks, yet essential, are frequently impacted by recurrent disruptions such as public transport failures, adverse weather or strikes. Flexible transit systems can be used to limit the impacts of recurrent disruptions on urban mobility. In this study, we examine the potential of on-demand park-and-ride systems to complement an existing transport infrastructure and improve network resilience. We formulate a stochastic park-and-ride facility location problem which captures the entire user trip chain from the origin to the destination via pick up and drop off nodes in a mobility network. We use a Logit model to capture users' mode choice between paths in the park-and-ride system and a reserve travel option. Stochastic scenarios are used to represent varying traffic conditions to recurrent disruptions. The goal is to maximize the expected ridership in the park-and-ride system by identifying the optimal location of pick up and drop off facilities and accounting for users' mode choice. We develop a customized Lagrangian relaxation algorithm to solve the resulting mixed-integer programming problem on large scale instances and quantify its performance through a sensitivity analysis by comparing it against a direct mixed-integer linear programming approach. Numerical results are presented on realistic instances generated based on the city of Lyon, France. Our findings show that the proposed methodology can provide key insights to support the deployment of park-and-ride systems and improve network resilience by capturing a significant proportion of users under disrupted traffic conditions.