You want to transport the same ESP8266 device between a number of locations. Each location has its own WLAN with a different WLAN/Password.
You are using the web server running on the ESP8266 (AP mode) purely to enter the credentials for the current WLAN. Once the WLAN credentials have been configured, the ESP8266 simply then fetches/sends data to/from (say) the internet. Is that all correct ?.
That is quite common and should all work. I have a number of examples, including clocks, which do this.
AP mode is needed to configure the clock, via its own web server, with things like Wlan credentials, NTP server, timezone etc. Once it has been configured, I can further update it via a PC browser via the WLAN and the device can update itself from internet based NTP servers.
Here is one example: Arduino ESP8266 Speaking Clock - Exhibition / Gallery - Arduino Forum