I've got it, I found that this methood worked best for me. For anyone else with a similar problem, this is the fix. The code below gets the item that has been selected then matches the item to my database and displays the name of that person(DataRow)......
Private
Sub EditButton_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles EditButton.Click
Me.Child_InformationTableAdapter.Fill(Me.Child_Information_DatabaseDataSet.Child_Information)
'Check which item has been selected'
Dim Count As Integer = Me.ListView1.Items.Count
Dim AddFromZero As Integer = 0
While AddFromZero < Count
If ListView1.Items(AddFromZero).Selected = True Then
Dim SelectedDataRow = Me.Child_Information_DatabaseDataSet.Child_Information.Rows(AddFromZero)("FirstName") + " " + Me.Child_Information_DatabaseDataSet.Child_Information.Rows(AddFromZero)("LastName")
MessageBox.Show(SelectedDataRow)
End If
AddFromZero = AddFromZero + 1
End While
End Sub