President Donald Trump Carlos Barria | Reuters

President Donald Trump will throw himself fully into his battle to overhaul U.S. trade deals this week with special counsel Robert Mueller's Russia investigation — mostly — behind him. The president won the White House in large part by pledging to crack down on foreign trade abuses and rework international agreements to boost U.S. manufacturing and protect American workers. The conclusion of Mueller's probe — and the Justice Department's decision not to charge the president with obstruction of justice — comes at a pivotal time in Trump's push to follow through on a campaign priority ahead of his 2020 re-election bid. Trump will try to rework U.S. trade relationships on more than one front in the coming weeks and months. He not only aims to strike a new deal with China, but also wants Congress to ratify a revised North American trade deal. A flurry of activity on the trade front starts this week: Canadian Foreign Affairs Minister Chrystia Freeland is set to meet with U.S. Trade Representative Robert Lighthizer and undisclosed members of Congress in Washington on Monday. She led her country in talks to revise the North American Free Trade Agreement, which the U.S., Canada and Mexico agreed to do last year. They hope their legislatures will ratify the deal — dubbed by Trump the United States Mexico Canada Agreement — in the coming months.

Trump is set to meet with lawmakers Tuesday about trade issues.

The House Ways and Means Committee's trade subcommittee will hold a hearing Tuesday titled, "Trade and Labor: Creating and Enforcing Rules to Benefit American Workers." Concerns about protections for workers have led to some resistance to the USMCA deal within the Democratic-held House.

Lighthizer and Treasury Secretary Steven Mnuchin head to Beijing on Thursday to continue talks toward a trade deal with China. Trump has touted progress toward an agreement with the world's second largest economy, which could end a potentially devastating trade conflict. The sides still need to hash out some of the finer points of a deal, such as how much China will increase its buying of U.S. goods, how the U.S. will stop Chinese intellectual property theft and how quickly the Trump administration will lift tariffs on $250 billion in Chinese goods.

A Chinese delegation led by Vice Premier Liu He will then come to Washington for more discussions starting April 3.

Trump is also deciding whether to impose tariffs on European cars. The Commerce Department sent a confidential report to the president last month that was expected to recommend duties on national security grounds. Some Senate Republicans who opposed previous tariffs levied using a national security justification have started to line up against the potential auto tariffs.

Trump has railed against China, Mexico and Canada's trade practices for years and sees the criticism as a central part of his political appeal. He now stands closer than ever to reworking trade relationships with all three countries as he looks for signature policy achievements to promote on the 2020 campaign trail.

Trump in a stronger position

Some trade policy observers believe the end of Mueller's probe — and Barr's letter saying the special counsel concluded that the Trump campaign did not collude with Russian efforts to influence the 2016 election — put Trump in a stronger position in talks with China. Of course, the president will still face some legal questions moving forward: Democrats continue to push for the release of Mueller's full report, while probes both inside and outside of Congress are still looking into Trump's administration and businesses. Potential pitfalls await the president on every front of his trade policy push. The U.S. and China still have a long way to go toward agreeing to a deal — and Beijing appears unlikely to meet some of the Trump administration's demands. Trump, who is fixated on reducing the U.S. trade deficit with China, wants Beijing to buy "double or triple" the $1.2 trillion in U.S. products it previously offered to purchase. It is also unclear how fully China will address U.S. concerns about intellectual property theft and forced technology transfers. Bipartisan lawmakers including Senate Minority Leader Chuck Schumer, D-N.Y., have cited the issues as the most important points in the China talks, and have signaled they could resist a deal that does adequately address them. Republican senators such as Marco Rubio, R-Fla., have been vocal about cracking down on Chinese trade abuses. Trump also said last week that he could leave tariffs on China in place for a "substantial period of time," even after the world's two largest economies reach an agreement. Reports have indicated that China threatened to pull back on certain concessions if the U.S. did not remove tariffs as part of a deal.

NAFTA 2.0 concerns

At the same time, Congress has started to scrutinize the terms of Trump's North American trade deal revisions. The House hearing Tuesday will try to assess how effective the U.S. has been in enforcing previous trade agreements, said Rep. Earl Blumenauer, an Oregon Democrat who leads the Ways and Means Committee's trade subcommittee. Blumenauer told CNBC that he has "some reservations" about a provision that would shield pharmaceutical companies making certain drugs from competition for 10 years, among other concerns lawmakers have about the deal. "These are areas that we want to zero in on," he said. "There are questions about labor enforcement, questions about environmental protections." "I want to find out if NAFTA 2.0 is any better" than the original deal, he added. The agreement went into effect in 1994. While Trump has pushed for swift ratification of the agreement, Blumenauer said the timeline for Congress to approve an agreement is "fluid." He noted that House Democrats are "not going to be bound" by "artificial deadlines." House Speaker Nancy Pelosi — who will play a large role in deciding whether the agreement can get through Congress — has also expressed skepticism about it.

A growing battle with the EU