Single wifi card, Connect to multiple access points simultaneously

Some(Most in 2016?) Wifi-chips can function in several modes at the same time, but all on the same frequency, because they use the same radio. Now, If you have 2 radios attached to your chip, you could have several functions on several frequencies/channels.

E.g. the Intel 3160 can be 1 station, 1 Access-Point, AND 1 P2P device at the same time. This is used for WiDi or Miracast, while still being connected to the "other" Network.

The valid combinations for your chip can be seen as root with:
iw list | grep -A 2 'interface combination'

The Intel 3160 returns:

valid interface combinations:
   * #{ managed } <= 1, #{ AP, P2P-client, P2P-GO } <= 1, #{ P2P-device } <= 1,
   total <= 3, #channels <= 1

Checking the USB-dongles within reach on my desk, I can tell you:

• rt2800usb reports:

      valid interface combinations:
           * #{ AP, mesh point } <= 8,
             total <= 8, #channels <= 1
  

• rtl8192cu dongles, that use the same chip as your device, report:

interface combinations not supported

This message means, that your card can only perform 1 function at the same time.

For some wifi-chips several signed firmwares with differing capabilities are available. AFAICT, not for your rtl819x though.

For an Intel IWLWifi a solution could have been to switch (one of the) connections to you being the AP, or making it "Ad-Hoc"

Otherwise you'd have to replace your card with one that has #{managed}<5 or similarly relaxed restrictions.

Or, add a(nother) 10€ WUSB-WiFi-dongle for connection to the second AP.

As close as you may seem to getting this to work, I am going to go out on a limb and suggest that this is not possible.

You do have the virtual interfaces set up correctly, giving you both a valid MAC address on the interfaces (layer 2) and good IP addresses (layer 3). However the actual connection to the AP is done over Radio Frequency, which is Layer 1.

Think of it this way, unless your wired ethernet card has two physical ethernet ports (RJ45, fiber, etc.) you can only ever plug into one network physically. The same goes for your wifi card.

Unless your Wifi card has more than one antenna (that you can control independently) then the Wifi card will only support one connection mode, either AP mode (receiving incoming connections) or a client (one to one). There may be Wifi cards that will let you do this, but it seems like this would need to be supported in firmware, not just in your computer's network stack (which you have properly configured).