+ you have to setup date
+ save, go in planning view - if you are not in the right view
+ and then calculate planning
Difficult to do more simple, except change milstone date directly in planning view (it is possible)
=> I known that this point is acceptable for a planner but for team members looks like complicated to explain
I thing it's a bad use case to have team member plan the project.
On the project leader should plan the project.
I try to use deliverable object but they are not displayed in planning view.
THEY CAN BE

It is the purpose on Global Planning view, introduced by V7.2
=> Add a button in milestone object view to reschedule planning ?
And why not in Activity ? in Test Session ? in Meeting ?
In my opinion, planning possibility calculation should only be triggered from planiing view.
=> Add object in planning view ?
It exists : it is the global planning view
NB : what you can do in your case is use the Automatic planning feature.
For instance, you plan a differentiazl planning calculation every hour.
Team member just updates milstones and doesn't bother any more, in the next hour the planning will automatically be recelculated.