hasso: Can't remember exactly, but wasn't there a limitation within certain versions of Windows or DirectX (?) that only permitted the monitor designated as primary to have hardware video acceleration? Don't know if this is the same situation as you are having, but sometime in the past (Windows XP?) I distinctly remember that if I played video on the secondary monitor it would jerk and pan scenes were crap, but if played on the primary everything worked perfectly.
Bang on. DirectX only supports DxVA (hardware acceleration) on the primary monitor. Check the codec that you're using and try and use something like CoreAVC (for h.264) that is really CPU efficient and doesn't necessarily require video card acceleration.