So I updated my old Minecraft world with the new Nether by deleting the DMI-1 and using the portal to reset the Nether. And it seemed to work, however now, for some reason, I can use my portal 1-5 times back and forth before the portal in the nether ends up linking to a brand new portal quite a ways away from my base. I don't understand why it would be creating a brand new portal after a random amount of usage when it was working moments before, any suggestions? I've tried moving my base portal and unlinking all portals but it ends up doing the same thing.
Unless this has changed in 1.16 (when you say new Nether I'm presuming that you are playing on a snapshot?) if you want portals to connect properly both ways the safest way is to build both of them yourself so that the coordinates matc.
The X and Z coordinates of the portal in the Nether should be 1/8 of the corresponding coordinates of the portal in the Overworld, the Y coordinate doesn't matter as much but if there are other portals nearby it is taken into consideration in calculating which of them is closest.
(Also, you can't port _to_ a portal above the bedrock ceiling in the Nether.)
When you use a portal the coordinates are converted (divided or multiplied by 8) and MC looks for portals within 128 blocks in the X and Z dimensions and if none are found a new one is created.
Because the portals have, at least, 2 obsidian blocks to stand on when porting each with its own coordinates it's possible for the left and right sides of a portal to connect to different portals in the other dimensions.
That may be part of the explanation, though it does seem a bit unlikely that that would happen twice (with your first portal in both positions.)