Would server load lower if I used two seperate sites?

I hope someone one could shed light on my question. My host provider (Bluehost) frequently shuts my site down temporarily with “excedeed cpu resources…blah wait a few minutes”. Although the page isn’t super busy or use a lot of plugins …I do have quite a few larger images I display with the plugin shutter reloaded or lightbox.

I also have another seperate website on another host provider. That website gets almost no traffic so I had an idea. If i uploaded all my images to website B and linked those images to my primary website A… would server load go lower on website A – evem though it still uses the image plugins shutter reloaded or lightbox? I know bandwidth would go down for website A but bandwidth is not a problem. Getting server load lowered is my primary concern and I do use wp-cache already. Could someone provide info on this area. thanks!