Each Portal Has a Unique Frequency:
The portals on Our Earth are operating differently than the portals in the parallel universe. It's a little like the portal system in Stargate, where the Earth portal has a human-made controller that operates slightly different from the rest.
Since your people are able to "Dial up" portal locations, there must be something unique about each portal - a coordinate system of some kind. The fact it was the fourth portal, and not the first/second/third is a coincidence. Something about the fourth portal had a coordinate system that was close enough to the ones in the parallel universe so they intermeshed. But while the coordinates used by the system in the parallel universe have additional numerics/symbols/mystic components that give them specificity to their own portals, OUR system operates with different coding, and is only partially compatible.
So once the fourth portal engaged the parallel universe one, our incompatible system intermeshed with theirs - badly. It started to cause malfunctions in the parallel universe, resulting in those random pots and things showing up here. The sheer volume of destinations in the parallel universe might cripple our portal system.
The real question is, what would happen if you disable the fourth portal? Would you be able to "disengage" from the parallel universe and start over, or Is there a higher-dimensional network which is now intertwined? In the first case, you could disconnect and solve the problem short-term, but run the risk of reconnecting to this or other parallel universes in the future (unless you can somehow figure out why the parallel universe portals weren't having this problem before, and copy it to create a separate network).
In the second case, the only "fix" would be to either shut down the whole thing or try to integrate better with the parallel portals. You might be able to stabilize and separate the portals by figuring out and copying their coordinate system. Then, our portals wouldn't send to theirs, and theirs wouldn't send to ours. It IS likely, however, that scientists/Enchanters on both sides would be working on figuring out what was going on. We could always use the "bad" coordinate system to tap into theirs, and eventually THEY would probably figure out what was going on and tap into ours.
At that point, the real fun of storytelling starts.