"The toy is between the two children."
Translation:장난감이 두 아이의 사이에 있습니다.
According to Tips & Notes: Number + Noun is one of the possibilities. So the counter can be omitted in this case.
because it's not really saying "children" plural as in "there are multiple children" you have to look at it in literal terms.
The subject is the toy, and it exists in the space that is between two children (as in what they are). The space that the toy is in, belongs to each child.