This paper presents an approach to provide strong assurance of the secure execution of distributed event-driven applications on shared infrastructures, while relying on a small Trusted Computing Base. We build upon and extend security primitives provided by Trusted Execution Environments (TEEs) to guarantee authenticity and integrity properties of applications, and to secure control of input and output devices. More specifically, we guarantee that if an output is produced by the application, it was allowed to be produced by the application's source code based on an authentic trace of inputs. We present an integrated open-source framework to develop, deploy, and use such applications across heterogeneous TEEs. Beyond authenticity and integrity, our framework optionally provides confidentiality and a notion of availability, and facilitates software development at a high level of abstraction over the platform-specific TEE layer. We support event-driven programming to develop distributed enclave applications in Rust and C for heterogeneous TEE, including Intel SGX, ARM TrustZone and Sancus. In this article we discuss the workings of our approach, the extensions we made to the Sancus processor, and the integration of our development model with commercial TEEs. Our evaluation of security and performance aspects show that TEEs, together with our programming model, form a basis for powerful security architectures for dependable systems in domains such as Industrial Control Systems and the Internet of Things, illustrating our framework's unique suitability for a broad range of use cases which combine cloud processing, mobile and edge devices, and lightweight sensing and actuation.