First note: CPEs are great for long-range PtP setups (this requires two CPEs to create a link over the air) or for a short-range PtMP setup (then one CPE could feed consumer devices). A stable link between a CPE and a hotspot therefore depends on the type of WiFi device the hotspot is using (I bet it's a device with omnidirectional antennas) and the distance between the hotspot and the CPE: if the distance exceeds the the range of the area covered by the hotspot, the hotspot's WiFi signal might be too weak for a stable communication.

Second: hotspots often use captive portals which might need to see the MAC addresses of the clients. Using CPEs in router mode in between will break this scheme. You should use client and AP mode for the CPEs.