I would either
A: work in a 4096 space in Fusion, and during your node process, spit the clips into their two 1920 sizes, work on them, and recombine them into the 4096 for render.
B: open the clips in a standalone version of Fusion, make your two 1920×1080 effect shots, and bring those into Resolve as new sources.
C: set your timeline in Resolve to 1920, put your top and bottom clips next to each other instead of on top of each other, and create a Fusion clip with those two clips. In Fusion do what you want to do to each clip and create a new saver for each one then bring those back into Resolve as source clips.
Personally I would just use B: Fusion connect can be handy, but sometimes its nice to just have a clean fusion comp on hand for tweaks and adjustments without having to go through the Resolve timeline.
Glenn