How to upload videos to iPhone and iPad using any Mac or Macbook that I have?

It seems that nowadays, the only time I hook up my iPad or iPhone to a computer is when I need to upload some videos to the Video app on iPad/iPhone so that I can view them offline.

I started uploaded some videos using a 256GB Macbook Air to the iPad and iPhone (both of which has 128GB). Next time, because the Macbook Air has only about 1GB disk space left, I tried to use my Macbook Pro to upload the video, but it couldn't -- when I drag the video to the "Device" section on iTunes, the video icon will bounce back to the Finder window -- it seems that I could only use the Macbook Air to transfer because somehow, it is "tied to that iPad/iPhone".

My question is, can I actually upload videos to any iPad/iPhone I have, using any Mac that I have? I have Macbook Air, Macbook Pro, and Mac Mini. And it will be best to no need to store the video files on the Macbook Air, for example, say if my Macbook Air only has 1GB of hard drive space left, and at home, I transfer a 500MB video to the iPad/iPhone from a hard drive that is on my home network or on my Airport Extreme's hard drive, then I wouldn't want the 500MB to occupy space on the Macbook Air after the video is transferred.