The stuttering playback may be caused by your i5 processor that might be a bit underpowered for processing 4k movies, particularly the 4k 60fps that is not supported by iMovie. iMovie supports 4k 30fps but not 4k 60fps. Also, you may have a lower end graphics card. The HEVC h.265 format that you are using can sometimes be problematical as well. Finally, the .mov format might be an issue, because .mov is just a bucket that can contain any number of different codecs from one .mov file to the next.
I am running Mojave with iMovie 10.1.12, but with a higher powered i7 MacBook Pro, and my 4k 30fps Mp4 videos play fine both in QuickTimePlayer and iMovie. I have a Navidia Get Force GT 650m graphics card.
You said that you are using iMovie 10.1. I take it that you mean 10.1.12 or higher. If not, update your iMovie and that might cure the issue.
Another thing that you can do is re-encode the video clips to something less than 4k. You can do that with the free download Handbrake, re-encoding to H.264, Mp4/AAC. You can get Handbrake here:
https://handbrake.fr/
A simple way to do it is to open Handbrake and do a File/Open Source. Navigate to your video and choose it as the source from the resulting screen. Then do File/Start Encoding. Wait a couple of minutes for the conversion to complete. Then save and import the converted clip into iMovie. See if that works.
When you share out from iMovie, in any case, the stuttering likely will be gone. Can't be totally sure, but you could try it to see.
-- Rich