These aircraft and controllers have their own dedicated and secure WiFi link. It is independent of all other WiFi services. You don't need any other WiFi to fly. You could fly it on the moon if you could get there and it had an atmosphere!
The 5.8gHz Video link is using the small antenna in the middle of the ST16s. Are you using the "Mushroom" antenna, or the small square patch antenna? It makes a difference in how the antenna is orientated. The top of the mushroom antenna needs to be pointing straight up to the sky, and the face of patch needs to point at the aircraft. almost a 90° difference, and enough to cause the signal to drop out prematurely it the alignment is that far off.