Please, my question is at the end of this formulated problem.
In the case of the twin paradox, the travel can be made without never accelerating higher than $g$. So the one who remains on the earth will always be subject to $g$, while the traveler can be under $g$ only for some part of the trip for example:
First he leaves earth, after overcoming $g$, and keeps accelerating at $g$ for 180 days, where he reaches around $0.508 c$;
Then the acceleration is removed and he travels at $0.508 c$ away from earth for 5 years;
After this, G is applied in the opposite direction for 180 days so that its speed in relation to earth slows down to 0 m/s;
When the relative speed to earth is null, the traveler spends 1 day slowly rotating 180 degrees, so that he points back to earth;
Then he starts accelerating at G for 180 day again;
After that G is removed and he travels at constant speed of 0.508 C for 5 years towards the earth;
At the end of this 5 years a contrary G force is applied for 180 days, so that he can slow down and return to earth;
Now he traveled at constant speed for 10 year, and during this period of inertial trip, his time suffered dilation of 1.16 as supposed by the observer on earth. But he also supposes that the time on earth was extended.
During this 10 years + 720 days + 1 day he was subject to G for 720 day (Never more than G);
Meanwhile his brother on earth was subject to G during the whole time;
Who really suffered time dilation and why? What causes time dilatation, speed or acceleration?