My question is, what if the A.G. simply refuses the orders of the Congress? For example, he locks himself away, or orders his personal security to defend him from the legislative branch? Is there any precedent for such actions? I imagine it would be handled by the judicial branch, but I am unsure due to President Trump's claims that he "owns the supreme court" (referencing how there are more conservative judges).
Per Denis' answer, that could happen. If congress is willing to escalate, they could impeach the Attorney General. Indeed there are already calls for his impeachment (from an NBC opinion column, but still):
By repeatedly demonstrating his bias in favor of Trump, by discrediting and misrepresenting the Mueller report and by refusing to provide the House Judiciary Committee with an unredacted copy of the 448-page document, it may turn out to be Barr who will soon face an impeachment proceeding in the House.
This all follows the, now famous, Speaker of the House saying that what Barr did amounted to lying, which she pointed out is a crime:
The House speaker, Nancy Pelosi, the top Democrat in Congress, accused William Barr of lying to Congress on Thursday and said neither the attorney general nor the Republican president were above the law.
'That's a crime,' Pelosi said, although she did not specify the comment to which she was referring.
So what does it take to impeach? From Wikipedia:
At the federal level, Article I, Section 2, Clause 5 of the Constitution grants to the House of Representatives "the sole power of impeachment", and Article I, Section 3, Clause 6 grants to the Senate "the sole Power to try all Impeachments".
The House debates the resolution and may at the conclusion consider the resolution as a whole or vote on each article of impeachment individually. A simple majority of those present and voting is required for each article for the resolution as a whole to pass. If the House votes to impeach, managers (typically referred to as "House managers", with a "lead House manager") are selected to present the case to the Senate.
After hearing the charges, the Senate usually deliberates in private. The Constitution requires a two-thirds super majority to convict a person being impeached.
So, is impeachment likely? No. Is it possible? Yes. Why is it not likely but still possible? It requires a supermajority in the senate, meaning at least a significant number from both parties have to support it. Aside from foreign policy decisions and military actions, the Congress of the US is not very bipartisan and as such impeachments (but also other bipartisan efforts) often fail.