Explain the ending of Niven & Pournelle "Footfall" to me

This is a question about the ending to a story so spoilers should be self evident.

In "Footfall" after engaging a wildy complex cast of characters in an endless plot exposition the story is bizarrely & summarily wrapped up in 3-4 paragraphs with (it appears),
the US President being forcibly overruled by his staff, and the decision being made (by staff & advisers) to crash the big atom bomb powered human ship into the alien ship instead of negotiating a surrender with the aliens- The End.

Is that correct or did I miss some nuance of the ending?

I should have added

…and yet the story ends with the alien commander surrendering to the earth people aboard the alien ship. So which is it… does the alien ship get destroyed by the earth ship on the edge of ramming it, or is mutually assured destruction somehow avoided?

As I recall, neither ship was destroyed, but the aliens realized that they were beaten. Their commander tried to “surrender”, human-style (with the intention of reneging on the surrender once it was safe to do so). The humans realized that it wouldn’t be a binding surrender unless it was done Fthip (is that right?) style- the human foot crushing the alien leader’s chest. Once that was done, the aliens had effectively become part of the human herd, and couldn’t go back on their word.

In other words, the humans conquered the aliens.

I get all that, but while that’s happening the human ship is still approaching intent on destroying them, and the US President’s ability to call it off from ramming the alien ship has been effectively squelched by the rebelling staff, so it appears the ships are still going to collide and destroy each other

No, it’s clear that there’s still time. The deadline you’re thinking of is that the Michael had passed its point of no return. Without assistance from Thuktun Flishithy the humans couldn’t get home.

So when the Fithp surrendered their first act would be to rescue the crew of Michael.

My take was the Fithp offer to surrender was genuine, but their terms were that they would rule the rest of the solar system while humans kept Earth. The smart people knew they could do better than that.

Just to clarify, the “foot on the chest” thing is s just a symbolic ritual that the Fithp, being herd animals, use to display dominance over each other. The humans are invoking the Fithp submission instincts (like making a dog roll over and expose its belly to you, I guess) rather than literally crushing the leader’s chest and killing him.

An aside:

In his collection of stories and essays N-Space, Niven mentioned that in the first draft of the book, the President’s advisors (Sec of Defense?) kill him at the end to prevent him from accepting the Fithp’s conditional surrender. His editor convinced him to modify that into them just imprisoning him and removing him from power.

You may also be confusing the atom-bomb-powered ship with the Space Shuttle, which was used to ram the Fifthp ship.