It’s a much longer book, and only part of it covers the question, but “The Rise and Fall of the Third Reich” by William Shirer also covers this in great detail–Shirer was a foreign journalist who lived in Germany during the time, smuggling his writings out in December 1940 when he realized staying any longer could be problematic.
Anyway while your sequence of events is it in broad strokes, it could maybe stand with some beefing up.
Firstly, prior to the Reichstag Fire things were already well under way. At no point in free elections in Weimar Germany did the Nazis ever attain a majority of the seats in the Reichstag, and Hitler had himself lost popular election to the Presidency losing to WWI General Paul von Hindenburg, who nearly won > 50% of the vote in the first round and clearly won it in the second round. Hitler won 30% and 36% in the first/second rounds respectively.
The Nazis were the single most popular party in Germany, but under the fractured politics of the Weimar Constitution they were never a majority party. However being able to take over the country required them to do a few important things prior to it all going down. Firstly was Hitler developed the idea that the Nazi party must be a “state within a state”, i.e., it needed to have some form of every organ of the State itself, so that it can quickly take over the state when the time comes.
Most importantly for elections, it had essentially its own army. The famous brownshirts of the SA, while the Communists also had militants who were engaged in skulduggery it was nothing compared to the SA. The SA were the most powerful and effective intimidation/paramilitary force in Weimar Germany (a country that sadly had several such groups representing political movements, to the long term instability of it as a democratic country.) The brownshirts were important because they kept any of the major opposition parties too weak to give the real power brokers in Weimar Germany (the Wehrmacht, more or less) any real alternatives. The DNVP were important partners that enabled Nazi Germany to come into being.
The DNVP were a reactionary conservative party, a coalition of monarchists, right-wing nationalists, anti-semites and such. But they weren’t really a “revolutionary” party, they mostly wanted a “return to how things were” versus Hitler’s party wanting a fundamentally different society. The DNVP had several of the important industrialists who were important in Hitler’s early rise to supremacy (Fritz Thyssen), and also connections with the Reichswehr. Both times when Hitler’s party needed to form a coalition government under the Weimar constitution it did so with the DNVP, and several of the DNVP’s leaders survived the transition to Nazi Germany and even found themselves in important political positions (most notably Franz von Pappen.) While Paul Hindenburg ran as an independent as President, his personal philosophies and political allegiances were closest to those of the DNVP, and many of his closest political friends were in the DNVP.
Under the Weimar system, the Chancellor is appointed by the President. The President is not compelled to appoint a Chancellor just because he has a plurality of seats in the Reichstag. Part of the reason Hitler had ran for President against Hindenburg, is Hindenburg was always skeptical of Hitler and the Nazis. He was part of the conservative old guard, and never wanted Hitler as Chancellor. Hitler felt if he was President, he’d be able to easily select an underling like Goering as Chancellor and he’d quickly be able to seize control of the country.
When Hitler lost the Presidential election in 1932 there were a series of short-lived Chancellors appointed by Hindenburg who were not Nazis. They were so short lived because with Nazi opposition there simply wasn’t significant power in the Reichstag for their positions to be tenable. Finally the DNVP’s leadership (notably Franz von Papen) speak with Hindenburg about Hitler. Franz von Papen proposes Hindenburg give Hitler the Chancellorship because it was obvious at that point any other scenario, the Nazis with some 43% of the seats would simply prevent anything from getting done. He proposed himself as Vice Chancellor, and the cabinet would be heavy on non-Nazi conservatives. It was pitched to Hindenburg that von Papen would keep the leash short on Hitler, and since the DNVP was closer with the army and no one was closer with the army than Hindenburg, they’d never have to fear Hitler getting out of control. Plus, at the end, the President can fire the Chancellor. The President under Weimar didn’t have a ton of day to day responsibilities but was incredibly powerful.
The last “free” election in 1933 was done with Hitler as Chancellor and was designed to get the Nazis an outright majority in the Reichstag. Hitler would use this to end the “shared” government with the old-school conservatives, and he’d then be able to do what he’d always longed to do, which was completely rewrite Weimar into the kind of regime he wanted. The Reichstag Fire was set not long before the election, this was enough to get Hindenburg to agree to the Reichstag Fire Decree, an important step in the end of a democratic Germany. But it still wasn’t enough for Hitler to win a majority in the Reichstag–and you better believed he used every power legal and illegal to try and get a majority in that final election.
Immediately after the election, Hitler began work in getting the Enabling Act passed. It required 2/3rds of the Reichstag to pass due to it technically being a constitutional amendment. But the RFA had given Hitler the power to arrest and essentially dissolve the Communist party and to severely limit the Social Democrats. He only really needed the Center Party to come to his way of thinking, the CP was a Catholic moderate party and while it’s unknown specifically what Hitler promised, he made promises to their leader sufficient to get them to sign off on the Enabling Act.
Once the Enabling Act passed, Germany was now legally a dictatorship for a four year term. However Hitler still had one check remaining on his power–the President. Importantly the President was Hindenburg, and the Reichswehr never in a million years would have sided with Hitler over Hindenburg. Hindenburg had the legal power to remove Hitler up until his death, and had he executed it, he likely would have succeeded in doing so because he would’ve had the full support of the army. But in the end, Hindenburg wasn’t really committed to democracy. He was skeptical of Hitler, but he also wasn’t a fan of the Weimar Constitution. For those who voted for the Enabling Act many saw it as a chance to draft a more amenable constitution, most didn’t actually expect it would result in a complete transformation of Germany into a Nazi State, it was always thought that the traditional powers would have a check on Hitler that would stop it from going that far. But the one thing not on the side of the traditional conservatives was time, Hindenburg was over 85 years old, and in the last year of his life he became increasingly infirm, and of course in 1934 he died. With his death went any reason for Hitler to show restraint, and with no Hindenburg there was no longer a clear alternative to Hitler in terms of having control of the Reichswehr. Hitler had been working for some time on building closer relations with the military, and since Hitler kept the office of President vacant at first, and later merged it with his own, he de facto became commander of the armed forces when Hindenburg died.
So it’s worth understanding, I guess in summation, that one of the keys to Hitler’s power was his politicking skills with his traditional conservative allies in the DNVP, and also at the end his politicking with the Center Party Catholics.
