Maybe I'm missing something right now, but
a) How do I move an entity by script? (with full event support)
b) how do I tell Even Pickier Dollies that an entity has been moved (by script)? so EPD can raise the event

for this I would suggest 2 new functions for the remote interface:
move_entity(entity_name: string, new_pos: MapPosition)
raise_entity_moved(event: epd.Event)

BTW further suggestions (only short, this is rather new suggestion threads)
a callback request_entity_move so a mod can implement the move by self
some “rotate” functionalty,like the methods/events for move

Not sure what you want to do. Do you want to drive EPD from a script? Or is that for an entity that you want to be moved by EPD and being notified?

If you want to be notified, register your entity like this:

script.on_event(remote.call('PickerDollies', 'dolly_moved_entity_id'), picker_dollies_moved))

This will register a callback for any entity moved. You will receive an event as described here: https://github.com/hgschmie/factorio-even-pickier-dollies/blob/main/API.md#event-callback

This will happen after your entity has been moved by EPD. It is intended to update internal state of your entity (e.g. move hidden entities around, update state etc). moved_entity will represent the entity moved in the new position and start_pos will show its original position.

The callback is always initiated after the player has moved an entity. There is no way to initiate a move e.g. from a script.

I have actually written exactly what I want, I don't know how else to formulate it!

trying again
this is a request for a NEW feature
in a mod I want to move an entity, simulating a player moves a entity by using the shortcut
and I thought there might be an interface for it in EPD like remote.call("PickerDollies", "move_entity", ...)

ah. that is an interesting idea. I won't get around to implement that any time soon; I finally want to get to porting LTN to 2.0 so I can continue playing my megabase. ;-)

Please file an issue here: https://github.com/hgschmie/factorio-even-pickier-dollies/issues; I will look into it next time I am touching EPD.