I'm aware that the twin 'paradox' is generally just a mistake of (mis)treating the traveler's frame as an inertial one, whereas it isn't, because he accelerates to make the turnaround. There just on detail I can't get. I apologize for the length, and thanks to anyone who bears with me.
I've been looking at a great website for relativity simulations, https://www.refsmmat.com/jsphys/relativity/relativity.html. It shows multiple observers, and all clocks from each one's frame of reference.
For the twin 'paradox', it shows the duration of the trip from two inertial frames: 1) the twin who we call the one 'at rest' 2) an observer that passes #1 as the traveler takes off and 'moves' in sync with him, but does not make the turnaround with him. The simulation assumes instantaneous acceleration, and the traveler makes the turnaround at t=50 on his own clock - we can say that this was agreed upon from the beginning.
From #1's perspective, the traveler accelerates to .866c and makes the turnaround at t=50, which is t=100 for #1. The traveler continues at .866c until he comes home. His clock shows t=100, and #1's shows t=200.
From #2's perspective, the 'home' is travelling away at .866c, the traveler decelerates to 0, waits t=50 on his clock, then accelerates to .99c. He arrives home at t=400 on #2's clock. From #2's perspective, the turnaround happened at t=25 on #1's clock. The math works out approximately: according to #2, the 'home' was travelling at .866c * 400 units of time, giving a distance travelled of 346.4, and the traveler raced towards #1 at .99c * 350 units of time, giving 346.5.
What bothers me is like this:
Presumably, all parties can know how much fuel was taken on board and what amounts were expended. From the home perspective, 33% of the fuel was used accelerating to .866c, 33% reversing the acceleration, and 33% accelerating home. However, from #2's frame, 33% was used decelerating from .866c to 0, and after a wait of 50, 66% was used to accelerate to .99c. For arguments sake, let's give the spacecraft a mass of 1kg. At .866c its kinematic energy is 8.986×10^16J. So, 33% of the fuel was expended to transfer that much energy on the first leg. At .99c is kinematic energy is 5.472×10^17J - about 6x the energy of .866c. How could #2 explain how just 2x the fuel (the 66%) imparts 6x the energy?