Hello guys, I think I has just been able to pin down the problem.
I don't have AAWIRELESS yet (ordered it today

but when I have read that there is this problem with Xiaomi phones not having internet connection I was thinking about canceling the order, as I have a stock MIUI ROM and I'm not in a mood in changing ROMs (although I might consider it if there was absolutely no other way since wireless Android Auto is really cool).
I came across this thread and read through usedr's workaround and I thought I might try how the wifi connection/mobile data works on MIUI when a phone connects to a wifi without the internet connection.
I have a wifi network at home where an internet connection is not allowed (for home cameras etc. which I don't want to connect to the internet) so I have connected to that wifi. The dialogue with the "switch connection" came up, of course.
Then I completely removed my regular home wifi and only left the non-internet one. I have disconnected and connected back to the wifi without internet and boom, I got the dialogue with "use mobile data".
Next, I have added my regular wifi back and tried it again. "switch connection" again...
So I have disabled auto connect to the regular wifi in the wifi settings (there is "auto connect" switch right at the top when you go to the wifi details), tried it again and that's it! I was once again getting "use mobile data".
So, TLDR: The MIUI won't let you use mobile data if there is another wifi connection available around you which 1. you have properly set up in the phone and 2. it is set to automatically connect.
Thus, there is no elegant solution, but if you disable autoconnect to any wifi connection you might be around when you are connecting to the AAwireless wifi, you will always get "use mobile data" option.
Second option is just to drive away far enough from any wifi you might have access to and connect to the AAwireless just then.
Hope it clears at least something. Those of you who have the AAwireless, please confirm that this is the case, I am almost 100% sure it works as I explain but can't try AAwireless yet since I dont' have it
