Automatically turn on/off data when downloading MMS
Again something tasker is able to solve (and maybe one of its "free alternatives" such as llama as well – but as a Tasker user, I can better describe it for that):

Both apps can act on events, and execute tasks. So let me construct a fake-profile (use it as "guide", not literally):


Condition:

Received Text (Tasker does not differentiate between SMS and MMS here)

Task:

Mobile Data → On
Wait → 1 min (set a time frame sufficient to connect and download the MMS)

Exit-Task: (optional)

Mobile Data → Off



The Exit-Task is optional. By default, Tasker restores the "before-state" automatically.

So what would this do? Whenever a message (SMS or MMS) is received, it would turn on mobile data for a minute to download the text, and then automatically switch it off again.

As I'm not sure whether an incoming MMS would even be signaled with data off, let's have a "Plan B":


Condition:

State→Mobile Network is On

Task:

Wait → 10 min (adjust time frame to fit your needs)

Exit-Task:

Mobile Data → Off



This would be a kind of "don't forget me" timer: If your girlfriends mother turns on data to receive the MMS, and forgets to turn it off again, it would automatically be turned off after the configured time-frame. Here the exit-task is mandatory, so Tasker does not restore the "before-state".