"allows them to play" should be accepted, too.
Bedstemoderen is actually the correct word for bedstemoren
Jeg troede at "moder" er mere gammeldags måde at skrive "mor".
Ordbogen siger at begge er ok: https://ordnet.dk/ddo/ordbog?query=moder
There was not correct answer which we are supposed to choose!
According to ordnet.dk, the pronunciation of "lader" is [ˈlɑ].