The outdoor sensor from Atlas or from any other weather station brand does not use WiFi. It sends the data over a one way radio signal or RF. This is not WiFi. This RF is picked up by a console by that manufacture. Then the console can connect to your network via WiFi or Ethernet (depending on model) to then send the data to the Internet weather services, or in some cases you can use other software/hardware to pick up that data on your local network. So the only part that needs WiFi connectivity is the console if it has that option. Unfortunately in the case of the Acurite Atlas that would be the Access device but that connects via Ethernet only. So both the Access and the display console are both picking up the RF from the outside sensor suite. But only the Access is connected to your network. But you can access your data from a mobile device over WiFi.
As for the device you mentioned from Ambient it is a Weatherbridge which is a rebranded Meteobridge and it is not compatible with the new Acurite stuff. From what I've read with the new stuff from Acurite you'll have to resort to the more complex methods you mentioned to report to other places than WU and myacurite.
There does always seem to be a lot of confusion about "radio" comms, RF bands, WiFi, etc. eh?
I actually had a recent 'chat' query with AcuRite support about Access access to IP WX sites, or even local ingest. Edited transcript below.
[Acurite does NOT support WX data transport to anywhere except WU and myAcurite.com.
Chat started: 2019-02-15 PM UTC
John: I recently bought a (5in1Pro 0614 sensor,, 0616 display, 09155 Access). Is there any way to have this PWS communicate with other weather services besides WU and Acurite? WX services like CWOP?
Customer Support: Thanks for your message, please wait a moment for an agent to become available and review your request.
*** Chris joined the chat ***
Chris: Hello
Chris:
At this time we only communicate with Weather Underground and Myacurite.com John: Does the Atlas model do so?
Chris:
Regrettably, it does not all our online devices only work with Weather Underground and Myacurite.com ...