Hi Jörg,
I'm not sure I've figured out your issue.

This is a summary of the (Google) translation:
1. Your mount is rightly synced/aligned (and starting coordinates are right) but after any GoTo command you don't find the target centered as expected.
2. If you manually center the target by the hardware handbox (without any new sync) then all subsequent GoTos work as expected.
3. While moving the mount by the hardware handbox (as at point #2) you see no ASCOM coordinate changes.
The reason why you see no ASCOM coordinates changes as soon as you are moving the mount by the hardware handbox is the (finite) low polling rate.
The hardware handbox is pretty useless while mount is being controlled by ASCOM; so I see generally no reason why asking (by PC) the LFEP to tell its position if you're changing the position by the PC itself...

This is the reason why I:
1. added the "silent" option to reduce traffic as much as possible;
2. set a low polling rate (1/10s) as default value (when silent mode is disabled);
3. added a slider to increase polling rate in case of need.
So if you like to move the mount by the hardware handbox be sure to disable the "silent" mode; if you also prefer less "latency" you can increase polling rate by moving the slider inside the Motion Controls panel.
With
Silent mode disabled you can see that if you move the mount by hardware handbox (at default polling rate) you'll see ASCOM coordinates updated as expected within 10s.
So there is no "misalignment" you've to "erase" by a manual movement...
Keep in mind the driver simply sends a GoTo command. It's the controller to move the mount according to (its) current coordinates and target coordinates.
I make an example trying to be clearer:
Let's say you're pointing at RA 01h 00m 00s, Dec +00° 00′ 00″ (so that the hardware handbox displays these coordinates) but ASCOM driver position is wrong (e.g. RA 01h 10m 00s, Dec +00° 00′ 00″).
You then send an ASCOM GoTo command to RA 01h 00m 00s, Dec +00° 00′ 00″. The mount won't move at all...
You'll see ASCOM coordinates will be refreshed (also in silent mode) as the driver "thinks" the mount is slewing because of the GoTo command.
Please let me know if I didn't figure out your issue...
CS
Armando