I'm a little bit confused about the problem here. The relationship class split policy determines what happens when an origin feature is split, not what happens when a destination feature is split. From the doc:
The relationship class split policy determines how records in the related destination table are treated when a feature in the origin feature class is split during the editing process.
If you split a destination feature, the newly-created feature should have the same foreign key value as the original, automatically relating that feature to the original table row. I just created a quick table:polyline relationship to verify this (using Global ID / GUID fields), and splitting a destination polyline resulted in two relationships from the origin table row.
Is there another factor in your scenario, e.g. attribution on the relationship class, attribute rules, or something unusual about your key fields?