Act 4, scene iii, why is Malcom not ready to express his grief in front of common public? Why does he want to go to a lonely place?

This scene is full of sorrow and grief.  First Macduff expresses his pain over the plight of Scotland.

"New widows howl, new orphans cry, new sorrows
Strike heaven on the face, that it resounds
As if it felt with Scotland and yell'd out
Like syllable of dolour." (Act IV, Scene III)

Malcolm is careful not to express his own sorrow over Scotland because he is not sure of Macduff's loyalty.  He feels that he should protect his position until he is sure of those around him.  He receives proof of Macduff's loyalty through the dramatic news brought by Ross.

Macduff learns that his family has been murdered. 

"Your castle is surpris'd; your wife and
babes
Savagely slaughter'd; to relate the manner,
Were, on the quarry of these murder'd deer,
To add the death of you." (Act IV, Scene III)

Malcolm is then convinced that Macduff is, in fact on his side.

"This tune goes manly.
Come, go we to the king; our power is ready;
Our lack is nothing but our leave. Macbeth
Is ripe for shaking, and the-powers above
Put on their instruments. Receive what cheer
you may;" (Act IV, Scene III)