Got exactly the same problem. Tried Windows version from CD, but it have problems as u mentioned. Can you provide 2.0 exe file? What bugs have been improved in 2.1?
Hey, so the original PoL exe you can find inside your GoG installation of DOS HoMM 2. It is inside the file homm2.gog which is actually an iso file that you can mount with windows 10 or daemon tools. Rename it to iso, mount it and you can find the original exe there, called HEROES2.exe. Replace your exe with the one from homm2.gog and you can enjoy no stuttering when moving. Sadly it's not ideal.
Also in your install folder you can find README.TXT that shows you the patch info for 2.1. There's many fixes, so using 2.0 is a shame just to avoid the stuttering, but so far there's no other fix. :(
Here is copy pasta of patch info.
4) Patch info:
When you right clicked on a hero's scroll in the kingdom overview (summary) screen a "%" was displayed instead of the correct text. This has been fixed.
The original good and evil campaign cutscenes were truncated. The final frame is displayed now.
Right clicking on the square to the north of a tent also displayed the Traveler's Tent text. This no longer happens.
Having the Alchemist remove the Broach of Shielding from a hero did not restore the -2 power the hero had lost due to the broach. The hero's power is restored now.
The graphic for the Ultimate Staff was corrupt and has been replaced.
The bonus for the Necromancer castle shrine was not always working from turn to turn. The bonus now works correctly.
Wizard's Campaign, Map 4: Taking the castle Magic will now end the scenario.
Fixed a minor map error on The Price of Loyalty campaign map 2.
The Price of Loyalty Campaign, Map 3: You can no longer "sneak" through the trees and get to the Red Tent.
The Price of Loyalty Campaign, Map 8: Removed the shipyard from the landlocked necromancer castle in the south.
Descendants Campaign, Map 3: You can no longer walk around the Blue barrier.
Descendants Campaign, Map 4: Fixed a bad mine at x65,y3.
Descendants Campaign, Map 8: Fixed a bad mine at x61,y21.
New Enemies Map: Corrected a typo in the scenario description.
Sharkania Map: Fixed the mine at x40,y6.
Fortress Isle Map: Corrected a minor map error.
The computer heroes will now cast blind, berserk and paralyze spells.
The Visions Spell has been fixed. Previously if a group of monsters were willing to join you for gold, the amount of gold the spell said it would take to get them to join was twice the actual amount.
If the Ultimate Artifact has been found the tavern rumor relating to it would be incorrect. This has been fixed.
All Ultimate Artifacts now disappear when the hero carrying them loses a battle. Previously only the original 4 UAs would disappear.
Several spelling and grammar errors were fixed.
When right-clicking on the top of some castles the information shown in the quick view window would be from a different castle. This has been corrected.
Sometimes the spell name would be grayed out in your spell book even though you had enough mana to cast it. This has been corrected.
The DOS version was not properly setting the palette on some video cards. This has been corrected.
The DOS version's random number generator was not being initialized properly. Because of this some of the starting parameters for scenarios were always the same. This has been corrected.
Sometimes casting Mirror Image on a two hex creature would cause the game to exit unexpectedly. This has been corrected.
Sometimes when rapidly cycling through different towns the game would exit unexpectedly. This has been corrected.
It is no longer possible to have a luck greater than +3 while defending a sorceress' castle.
Sometimes while attacking a castle with a shooting creature incorrect text would be displayed in the message area. This has been corrected.
The shot counter for the Magi and Archmagi creatures was not counting down the number of shots remaining. This has been corrected.
The Curse and Mass Curse spells were not working properly. They have been corrected.
There was a bad mine in the map for the 3rd Roland Campaign. It has been corrected.
There was a bad crystal mine on the map for the 4th Archibald Campaign. It has been fixed.
An invisible mercury mine on the Heroes map has been removed. Computer Heroes were apparently "claiming" it.
Heroes II no longer uses DirectSound under Windows NT since it seems to cause skipping during the cut scenes. If you experience garbled sound during the cut scenes in Windows 95 try adding /W to the command line for launching Heroes II. This will force DirectSound to be turned off.