My take is that the seizing of the government could take place at the beginning of the act, end, In between, or not at all. You just need to focus on the change/progress instead of whether or not they obtain. You could focus on the progress of the coup itself (are they about to succeed? Are they not making any progress at all?) or how the law will change with new leadership or whatever. You can have them succeed in their attempt, but need to explore change/progress rather than Obtaining.
This is something I was thinking about the other day. It's probably goofy, but seems to apply here so I'll share it. i was wondering what someone being murdered in an OS story might say in different throughlines.
In an OS Activity they might say "please don't kill me" because killing is an activity.
In an OS Situation they might say "I don't want to die" because being dead is a situation. They might say the same thing if the story is about Chamging Ones Nature.
If they say "please don't hurt me" they could fit into Activity or Situation. The character in Activity is probably looking at the act of being hurt and means "please don't stab me". The character in Situation, though, may be looking at the situation and would mean "please don't leave me in a state of suffering by stabbing me."
So I think you can sort of hint at what you're exploring like this. So let's say you've written about your coup. Maybe the first line is a character saying to a crowd "We've taken the throne!" With no other context, I think this feels like Obtaining. But if that character instead says "I am your king now" it suddenly feels like Changing/Progress.