Tukukkk

If President Trump was to go to the U.S. Capitol Building for the State of the Union Address, and he was met at the door by the U.S. Capitol Building security personnel with orders to deny him entry, could he order the Secret Service to arrest these security personnel and then proceed to enter into the Capitol Building?

Although this scenario is very unlikely to occur, would Trump have the Constitutional authority to do so since he is the Commander-in-Chief?

Moreover, since he is the Commander-in-Chief, would the U.S. Capitol Building security personnel have to obey his orders to stand down since he is the Commander-in-Chief, or do they only have to follow the orders of the Speaker of the House?

The US President is Commander-in-chief of the US military.

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;

(from Article II section 2)

That does not make the president the direct boss of every federal employee. The Congressional Sergeants-at-arms, in particular (and their assistants) are employed by, and responsible to, Congress, not the President. The Secret Service is part of the Treasury Department, which is part of the Executive branch, but I am sure the President cannot order them to arrest someone who has not committed any crime. If such a thing were pushed to a direct confrontation, I have no idea where it would go, I hope we do not find out.

Article I Section 8 grants Congress the power (among a number of others):

To exercise exclusive legislation in all cases whatsoever, over such District (not exceeding ten miles square) as may, by cession of particular states, and the acceptance of Congress, become the seat of the government of the United States, and to exercise like authority over all places purchased by the consent of the legislature of the state in which the same shall be, for the erection of forts, magazines, arsenals, dockyards, and other needful buildings

That seems to say the ultimately Congress controls the District, and sets the rules there. There is also the provision in Article I section two that:

The House of Representatives shall choose their speaker and other officers;

which would include the Sargent-at-Arms, I think.

Article I section five says:

Each House may determine the rules of its proceedings, punish its members for disorderly behavior, and, with the concurrence of two thirds, expel a member.

which again seems to grant control over the situation to the individual houses of Congress.

Article I section 6 says:

The Senators and Representatives shall receive a compensation for their services, to be ascertained by law, and paid out of the treasury of the United States. They shall in all cases, except treason, felony and breach of the peace, be privileged from arrest during their attendance at the session of their respective Houses, and in going to and returning from the same; and for any speech or debate in either House, they shall not be questioned in any other place.

Which again puts Congress out of the direct control of the President.

There is an underlying premise that the Capitol Police could lawfully exclude POTUS from the building. The Capitol Police power is created by 2 USC 1961, and includes the power to enforce certain sections of Title 2 Ch. 29, regulations created under that power, Title 40 Ch 51, and to make arrests for any violation of US law within the building. Were POTUS to enter the building for the purpose of speaking, that would not fall within the purview of the power of the Capitol Police. By 2 USC 5605, the Sergeant-at-Arms of the House of Representatives has the same law enforcement power as the Capitol Police. What is not clear is what it would take to make a POTUS appearance illegal: presumably the House passing a resolution to that effect, but that hasn't been done.