I like the idea of a prolonged Wilson administration. Any ideas that might help me develop the progress to full right-wing authoritarianism?
Makes most sense in the context of horseshoe theory (instead of a left-right political spectrum, you have it bent down so that the two extremes are almost touching).
However, there are a few different ways the authoritarians can become right wing.
First, changing standards. 100 years ago, eugenics was considered progressive. The "enlightened" view was that society would control reproduction so "superior" people would be born and "inferior" people would take their defective genes to the grave. That would be considered extreme right today.
Drug and alcohol prohibition were supported by some progressives, in coalition with religious conservatives. Have to protect people from themselves, as well as the evil greedy businesses that sell those products. Wilson didn't want to enact Prohibition but supported its enforcement after the 18th Amendment. We would just need a more aggressive police state at an earlier point instead of a change in policy.
Wilson was racist even for his time, and the 1920s saw a resurgence of the KKK. Having a friend in the White House might result in more Tulsas and Rosewoods, as well as federal laws restricting civil rights.
Authoritarians often (not always) pursue an interventionist foreign policy, and Wilson fit the bill in his second term.
Assuming the Depression still happens, you need a New Deal, or even better, Share the Wealth. After President Long dies, his underlings engage in rampant corruption. The Louisiana Hayride on a national scale. With the government even more economically powerful than OTL, crooked deals become the best way to get rich quick. Authoritarian regimes tend to be kleptocracies.
Most plausible sequence might be to have the GOP win in 1924 with Wilson retiring after three terms, in which federal police power is dramatically expanded and federal laws are passed in support of eugenics and white supremacy. The 1929 stock market crash happens in the summer of 1928 instead of the fall of 1929, so the Democrats paint the Depression as what happens when you give Republicans the keys. A Wilson style prog from the border south or Midwest beats Al Smith for the nomination and goes back to the fascist policies. Huey Long primaries the incumbent in 1932 and implements Share the Wealth. He cuts a deal with Japan to sell them oil, thus butterflying away Pearl Harbor and out involvement in WW2. Which in turn means black veterans don't have the argument that they spilled their blood for a country that treats them as second class citizens. Long serves three terms and retires in 1945.
Russia takes a bigger chunk of western Europe after WW2, making the communist threat more serious and denying us the ability to get rich off the Marshall Plan, so we need a tighter security state. No GI bill to help create a prosperous middle class, so you end up with Long's successors selling out to the likes of Standard Oil. (Crony capitalism is a key feature of fascism.)
I'm sure there are more experienced members who could improve on that, but it's a starting point.
ETA: A Huey Long presidency also creates an obscure but very important butterfly effect. IOTL, the fallen Kingfish was a hero to a young Minnesota liberal named Hubert Humphrey. Humphrey moved to Baton Rouge in 1939. He was appalled by Jim Crow and eventually became the leading civil rights advocate in Congress. With a Long presidency, he moves to DC instead and doesn't give the great speech at the 1948 convention (which in turn triggered the Dixiecrat walkout).
So we have the following differences from OTL:
Stronger tradition of centralized power
Much weaker civil rights movement
No Democrat schism
No anti-Hitler propaganda to remind us of our own faults
The Holocaust is either unknown to us or Germany and the USSR are blaming each other, so Nazi racial theory hasn't discredited eugenics
Virtual one party system
Without us trying to beat Hitler to the A-bomb, the USSR might get there first.
Stronger and more threatening Soviet Union (I had them take all of Hitler's occupied territory to maximize the threat, as the OP was looking for a more authoritarian US during the Cold War. With no US reinforcements, the WAllies might also have had to lay low and allow Hitler to devote more resources to the eastern front and force a stalemate, but that would make the Cold War less intense.)