Confirmed that having the relationship class removed allows for the split to work as intended. We don't edit this polygon that often, so for now my work around will be to remove the relationships prior to editing, and then recreate the relationships once I am done.
Doing some reading- I think this is what the error is that I am seeing:

This is a tad frustrating, but we can work around for now. Hopefully, once we upgrade, we can use the delete/insert/insert model and this won't be an issue anymore.