This work proposes a novel technique to align Object-Centric Process models and data integrity constraints from Entity-Relationship (ER) Diagrams, supporting data-dependent access control and guaranteeing data-integrity-by-design in the execution of a business process. Recent developments in process modelling and mining notations have highlighted how critical data objects affect the evolution of process models. Yet, few works have considered the integration of data relationships between data objects in object-centric modelling notations. As a consequence, object-centric process models (OCPM) may violate data-integrity and existential dependency constraints that are necessary for the deployment of models in information systems. We examine how OCPM can integrate access control, cardinality constraints, existential dependency, total participation, and structural integrity. In particular, we extend the semantics of one OCPM language, the Object-Centric Condition Response Choreographies (OC-DCR choreographies), to include explicit identities of actors and object deletion and extend the execution semantics to respect the ER model constraints. We illustrate the idea with a running example of an OC-DCR graph and an ER model for a small healthcare process.