In the end, I got it all working - with the patient support of @dibdot. A big thank you for the development and support of Travelmate, Dirk!
Solution / What I had to do:
- I deleted all Intefaces (Network -> Interfaces) except of the "LAN (br-lan)"
- I deleted all Wireless Networks (Network -> Wireless) except of the "Generic MAC80211 802.11bgn" (which cannot be deleted).
- I created a new, first Access-Point (AP) (Network -> Wireless -> Add)
- I added a Travelmate inteface "trm_wwan" with the Travelmate wizard (Services -> Travelmate)
- I did a network scan (Services -> Travelmate -> Wireless Stations)
- I choosed two networks ("Uplink SSIDs) with "Add Uplink" (Services -> Travelmate -> Wireless Stations)
That's all. From this point on my device was working like expected. Travelmate activates / deactivates automatically the available Client Networks (Network -> Wireless) as needed - no manual intervention necessary. Since I had troubles getting the web authentication login site from a specific hotspot (DNS resolution failed), I had additionally to do the following:
- Disable "Rebind protection" (Network -> DHCP and DNS)
or, alternatively - Add the domain name of the failing web auth login site to the "Domain whitelist" (Network -> DHCP and DNS).
Now, I can wireless access the Webinteface (LuCI) over my configured Access-Point, even my device is not connected to any hotspot. 
Great!