Terrestrial and satellite communication networks often rely on two-hop wireless architectures with an access channel followed by backhaul links. Examples include Cloud-Radio Access Networks (C-RAN) and Low-Earth Orbit (LEO) satellite systems. Furthermore, communication services characterized by the coexistence of heterogeneous requirements are emerging as key use cases. This paper studies the performance of critical service (CS) and non-critical service (NCS) for Internet of Things (IoT) systems sharing a grant-free channel consisting of radio access and backhaul segments. On the radio access segment, IoT devices send packets to a set of non-cooperative access points (APs) using slotted ALOHA (SA). The APs then forward correctly received messages to a base station over a shared wireless backhaul segment adopting SA. We study first a simplified erasure channel model, which is well suited for satellite applications. Then, in order to account for terrestrial scenarios, the impact of fading is considered. Among the main conclusions, we show that orthogonal inter-service resource allocation is generally preferred for NCS devices, while non-orthogonal protocols can improve the throughput and packet success rate of CS devices for both terrestrial and satellite scenarios.