Roei_l
One way I can think of is whenever the parent fills the response you can push every response as embedded data into the child's contact by creating a workflow of add to xm Directory and when the child fills the response all those embedded data's will be pre populated.
And use the child's information on dashboard to see both the parent and child's response.
This way you won't have to create any unique link. But a catch here is the above would work only if parent is filling first and then the child. If the child is filling first just do the same process but this time pushing child's info in parents contact.
Hope it helps!