Plane Shifted Dungeon - Feywild/Shadowfell - Splitting the party

So my group is coming up to their first big dungeon at level 5-6 and I wanted to do one where the party is shifted to different planes. Half the party shifts into the feywild the other half goes to the shadowfell. Both dungeons will be exactly the same and the party will still be "together" but on different planes. I am trying to figure out some ideas to have them interact with each other across the planes to finish puzzles, combat, and a bad guy at the end (Prince of Frost). I want the party to feel split but still be able to help each other across the planes also there is bot ha Shadar-kai and a Fairy in the party so they will already be familiar with both shadowfell and feywild. I have played similar encounters in things like WoW or other video games / Stranger things but not sure how to translate this to the table well. Any suggestions or advice would be greatly appreciated, or if you have run something similar! Also looking for maps that have both feywild and shadowfell versions if possible.