Hi,
Without knowing more detail on how you're updating the layers - What you should probably do is programmatically create a new local map service based on the new map package, start the service and create a new local dynamic layer then remove the existing local dynamic map service layer from the map, stop the existing local map service, and add the new layer to the map (either with the same layer ID as the previous layer or if it's a new ID you may need to update the legend map layers. You might like to try applying some transparency to the layers as you're removing one and adding the other in order that the transition appears smoother?
Cheers
Mike