Telehealth systems have evolved from single-institution digital tools into large-scale, multi-hospital infrastructures that support distributed clinical networks. This transformation introduces architectural challenges that extend beyond conventional mobile application development, requiring scalable, secure, and interoperable software systems capable of operating across heterogeneous healthcare environments. Despite the growing operational importance of such platforms, limited attention has been devoted to their mobile infrastructure design from a software engineering perspective. This paper conceptualizes multi-hospital telehealth platforms as distributed, multi-tenant software systems and proposes a scalable iOS infrastructure architecture tailored for clinical network environments. The study examines architectural patterns for modular mobile design, tenant-aware segmentation, backend interoperability with Hospital Information Management Systems (HIMS), reliability engineering under high-concurrency workloads, and cross-device ecosystem integration. By grounding telehealth platform design within distributed systems theory and enterprise mobile architecture principles, this work contributes a structured framework for building resilient mobile infrastructures in regulated, mission-critical domains. The architectural insights developed herein are generalizable beyond healthcare and applicable to other large-scale mobile platform ecosystems.