Your question, directly: would baking the textures fix the issue, is answerable by Yes. I think you need to know why. Any procedural textures have to anchor on to something. They have to know their location and scale. Generated and Object coordinates offer different locations and scales (learn more about those specifics as metaphor_set commented) as inputs. You've chosen one of each on aesthetics alone which is totally fine.
Personally, I'm not in the 'physically correct' camp because I think artistic tools are meant to allow expression and artistic expression isn't always physically correct; but you've proven something by commenting about Window as a coordinate input. You froze the position and scale of the procedural texture to the Window that's viewing the scene along the Z axis. Since you and the Window move together, the geometry is passing through a "cloud" of procedural texture so the movement is easier to mentally track. In a rough way, you've 'baked' the texture to the Window.
Well. The next best thing is to bake the texture to geometry that moves so the gloves or camera or coordinates don't move separate from the view or gloves. (Confusing, I know.)
You've found your happy still-frame that represents the position and scale of "Leather." Stick it! UV unwrap the thing; I see the settings "Leather" provide for Diffuse, Normal and Glossiness information and that would mean Baking/F3 Saving ALL those inputs OR, perhaps take a long, careful time to unwrap the glove along intelligently chosen seams and use UV as the coordinate inputs. This WILL once again alter the scale of your texture.
You might have to sacrifice using different Vector locations and scales (I don't fully understand that without knowing "Leather"). But, you'll get away from a texture that looks really dodgy and is moving about.
Image is identical texture three times changing only the Vector input to alter the scale and behavior.