Memorizza l'instanza di Form3 in un membro privato di Form2 e utilizzala quando stai per chiudere Form2:
codice:
'in form2
Private f As Form3

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
    f = New Form3
    f.MdiParent = Me.MdiParent

    f.Show()
End Sub

Private Sub Form2_Closing(ByVal sender As Object, ByVal e As System.ComponentModel.CancelEventArgs) Handles MyBase.Closing
    f.Close()
End Sub