How does Gertrude seek to shield Hamlet after the death of Polonius?

One of the central questions of this play is whether or
not Gertrude loved King Hamlet and was simply wooed or pressured into marriage with
Claudius, or if she already had some kind of relationship with him before the murder and
perhaps was even somehow complicit in getting rid of him in order to marry Claudius. 
That issue, as well as the haste with which she remarried, is at the root of the
Hamlet-Gertrude relationship and conflict.  Just as Hamlet is never really sure about
his mother's loyalties, neither are we.  However, we do know that after Hamlet confronts
her with a picture--literally--of both men, she is somehow broken and contrite about
what she's done. After this meeting, she does seem to ally with her son, at least to
some degree.  Here's how we know it:

Despite having just
committed the accidental murder of Polonius, Hamlet does reveal to her that his
"madness" is only an act, and he asks her not to tell.  When she leaves him and goes
straight to the King (Act IV scene i), she does tell about the murder but she continues
the charade of Hamlet's madness. 

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"Mad as the sea and wind when both
contend

Which is the mightier.  In his lawless
fit,...

And in this brainish apprehension
kills

The unseen good old man
[Polonius]."

She attempts
protect her son with the lie that he is, indeed, mad.