> So how would that event in the US have succeeded in overthrowing the government? What would the next steps have been? Even if they killed everyone in the building, would the rest of the government/military/courts/etc. agree to follow orders from the new kings? Why?

Here's how it would work:

The process for electing the president is that states certify their electoral college votes in what's known as the Certificate of the Vote. On 1/6 the certificates are counted and objections are raised. It takes one Senator and one Representative to raise an objection in writing, and Republicans had planned on objecting to Arizona, Georgia, Pennsylvania, Wisconsin, and Michigan at least. Objections are settled by voting in the House and Senate. Each chamber gets a vote, and if they agree the objection is sustained and the votes discarded. If they are split or disagree, the objection is overturned. Democrats had a majority in the House while Republicans had a majority in the Senate, so this would have went in favor of Joe Biden.

To succeed then, the Republicans needed to get outside of the regular Constitutional order. Their main objective on 1/6 was to delay the certification past that day. There is no precedent for this. At first Trump wanted Pence to simply refuse to certify the vote and then force the GOP friendly states to "recertify" their results. Trump only needed a few states to recertify to win. But Pence refused to do this, hence the chants of "Hang Mike Pence".

However, the invasion of the Capitol gave new life to this idea of recertification. The hope here was that if the proceedings were disrupted, we were in uncharted Constitutional territory. This would have given additional time for Trump to try and twist the arm of the various states, as he had been doing before 1/6 to the states of Arizona and Georgia (at least).

Once the states recertified their votes, they would have reconvened the Congress and VP to certify the election. This puts the Democrats in a tough spot. They could have let the "recertified" results stand, in which case Trump would win. Or they could object. If they did, then the Republicans could also object. This would throw the recertified votes out.

But here's the catch. If no candidate has 270 electoral college votes after the counting, then the matter is put before the House, but not in the normal way. Instead, each state delegation gets 1 vote, for a total of 50, with 26 to win. State delegations are decided by the states, and Republicans would have a 26-23 majority in this scenario (PA would have tied, if they don't agree their vote doesn't count). The House would then vote for Trump, and he could have been President despite losing the popular vote and the electoral college.

There's a lot that needed to go right for Trump for this to work, and that's why it didn't. But it went a lot further than it should have, and definitely broke a 240 year streak of peaceful transitions of power in the US. In fact, it seems like the only reason the vote was able to be certified on 1/6 is because Mike Pence refused to leave the Capitol with the Secret Service. Had he left with them when they wanted him to, the proceedings would have been delayed indefinitely.