"When an upper-class rebel is suddenly disinherited by his fed-up father, he struggles to win his father?s approval in order to have his inheritance restored, but his plans derail when he is forcibly drafted to fight in the second US civil war."

Good points about the two-headed logline. A suggestion that has helped me: backstory is the breeding ground for a good character flaw.

Consider splitting out one the inciting incidents as backstory (probably the disinherited part). Boil it down to a concise character flaw that will make the main action of the story very difficult for the MC in act II, but something he must overcome it in order to achieve the goal.

Spot on what Nir Shelter said about there being essentially 2 inciting incidents: being disinherited and being drafted.

And "the war of 2079" raises other questions that distracts from what might seem to be the premise of the story. The war of 2079? What war? How? Why? It might be better to just avoid mentioning the time frame. Leave that to the story proper. Because the human drama of a son trying to win back his father's approval by joining the military is timeless; it could take place in World War 2, in the Napoleonic Wars, in the Punic Wars for that matter. That it takes place in 2079 is irrelevant for the purpose of a logline unless there is something special, unique about the whatever happens 2079. In which case, it suggests the story is about something else, something greater at stake than a son's personal problem with his father.

Given the constraints of a logline, you really only have space to promote one idea, one plot thread, not two or three. What is the central idea of your story, the principal plot? The struggle to reconcile with the father? Fight in a war? A future civil war that takes place in 2079? What is the core plot around which everything pivots?

You keep making it longer by adding in descriptive phrases and vague notions of unclear actions?I'm gonna go back to my initial suggestion for how to summarize the major events and main character. You can change around certain words or details, but the idea is to tell us only what we absolutely need to know to have a basic understanding of the story's main concepts. If it's more than 25-30 words you're probably saying too much.

Let me put it this way: even a terribly boring or ridiculous idea can be summed up in a simple sentence. "An alcoholic dentist must knit a sweater before sunrise or a psychotic elf will turn his brain to pudding." This would make a really stupid movie, but do you have any questions about what's happening or why? You know the main character and a little something about him, you know his main goal, you know the stakes if he fails, and you know the antagonist. That's all you need. A synopsis would contain more plot detail, such as how this all started, the successes and setbacks he encounters while knitting, how it all turns out?but a logline only needs the very basics, and it must be simple & clear. Don't get fancy with it. An interesting story sells itself; all you have to do tell us what that story is.