Perhaps I misunderstand you but, if we have:
1. Twin A and B on planet P and point X, a fixed distance away from planet P.
2. A accelerates away from P towards X.
3. A accelerates towards P to stop at X.
4. A records the total elapsed time since 2.
5. A accelerates away from X towards P.
6. A accelerates towards X to stop at P.
7. A records the total elapsed time since 5.
Then all observers must agree on both recorded proper times recorded in step 4 and 7.