http://www.pcgamingwiki.com/wiki/Troubleshooting_guide/Input_problems plus Windows article page.
There is mouse acceleration that never work properly. And there is issues in all Windows that this sometimes turn back on randomly. Should be described somewhere on PCGW how disable it entirely or tweaked to make no differences.
Another solutions listed on this articles on URL. Look to other section too, not just mouse. Some input wrappers probably required for you. GOG have own GOG DX Wrapper but it differ from games release to release. Some most recent games/updates releases come with Dinput wrapper, most else and subj game fome only with Ddraw GFX wrapper.
Dont forget to configure this wrapper from dxcfg.exe or launcher. Make sure you launch them as admin.
If game or Galaxy client installed not to X/Games/ you must run client and games also as admin. And admin only. Put armin run to galaxy.exe or to GOG War2 Launcher (or BOTH!). Otherwise it will ignore what you configure or even maybe some dlls will be ignored.
Alays set Keep aspect ratio everywhere. That can affect mouse pointer too (thogh not the speed maybe).
Usually that additional utility apps are trash. And usually it is exactly them who bring issues. If there is no Frequency switcher on mouse maybe better install ot and setup. But exclude it from Windows autoload.
Logitec ulitilities known to bring issues for D1/Wc1-2. Terminate LogiOptions.exe process or any similar.