Personal Hotspot Disappears when iPhone connected to WiFi

My Kindle Fire quickly connects to iPhone5se hot spot when iPhone is not within range of an acceptable WiFi signal. Almost immediately after my iPhone locks onto a strong WiFi signal, my Kindle can no longer find my Personal Hotspot, so it appears it is being shut down by the iPhone. This is a problem when the in-range WiFi signal does not have Internet connectivity, and I am seeking to get Internet connectivity via the mobile phone wireless network. Is there a way to get the Personal Hotspot to operate while the iPhone is connected to a local WiFi signal, perhaps one that is providing airport boarding information.