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.