Replying to Fuji X-E1

So I purchased a Fuji X-E1 over the summer to try and get back into taking some pictures. I have only used an SLR so after doing some research this looked like one of the easiest cameras to use as it had a lot of manual functions that were easy to navigate and understand. For taking photo's it is great. I must warn you, I do not use it for skiing. I take pictures at some local bike races, use it for product photos in my store, and on vacations and such. For taking photos, it's great.

Lately, I want to try and make a few videos of some bike builds and parties that we host for our local club. Even with a tripod it seems to move in and out of focus at times and if I try using it by hand (very slowly, with a DIY stabilizer) it goes crazy. Now I know when I purchased the camera it came with the basic 18-55mm f/2.8-4.0 lens. I am shooting with a smaller aperture and my ISO isn't super high. The auto focus tends to go bananas if there is a change in light or I move the camera.

My question is... If I invest in a nicer lens, with that help at all with video? Or is it best to maybe try a different camera IF video is something I want to explore more. Any input/advice is greatly appreciated!