Liebling's cord blood will be tested as I'm A- and DH is A+. But neither of our parents were told with us what our blood groups were, we had to wait until we were old enough to donate blood before we found out (so I'm guessing MiL is positive, I know my mother is).

For donations, if you don't know (or rather, if the hospital don't know) your blood type then you're given O- blood as that won't cause any reactions. Yes, your blood will be tested for routine or nonessential blood donations so you get the right type, but in an emergency no-one worries about the blood type if you don't know it.