Can the President as Commander-in-Chief curtail or direct the activities of the Speaker of the House? Also, can he presume in his mind that he knows what activities the Speaker is about to carry out and thereby curtail them?
The US president is "Commander in Chief" of the US military only. This title is found in Article II Section 2 of the US Constitution.
The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States
The Speaker of the House of Representatives is not a member of the US Armed Forces, and so the president is not her Commander in Chief, and has no particular authority to direct or curtail her activities.
In recent events, the president has decided not to allow the speaker to use (at government expense) a military flight to visit Afghanistan. This is within presidential authority because the president is giving orders to the military, not to the speaker.
The BBC notes that in this current incident
The president was able to halt the trip by denying the use of military aircraft to Mrs Pelosi and a delegation.