The error message is right: and MDI child form cannot be modal - which is what the ShowDialog method is there to do.
If you want the main (MDI parent) window to "disappear" while the new window is visible, then it can't be an MDI child window, it must be a regular "top level" window - and then you just do this:
Dim mnf As New MyNewForm()
Hide()
Dim result As DialogResult = mnf.ShowDialog()
Show()