Translation:Our daughter does not play with their animals.
The daughter in this sentence is not playing with with animals that either belong to a third plural party (let's say neigbors] or belongs to her family and we consider all members of that family to be owners of these animals. So the animals are THEIRS, which in czech is JEJICH.
JEJI are hers but in nominativ, we need instrumental here. SVOJE could be only used if the animals belonged to the daughter and in such a case it would be SVÝMI to make it instrumental.