Though this love triangle has echoes of that in her latest film, ultimately the outcomes are very different. The choice Byrne made to give Swinton his blessing in order to preserve their love and family life for the sake of themselves and their children is as progressive as her partner's alternate choice in the film is archaic.
This makes it seem like Byrne is suffering, or at the mercy of Swinton's lifestyle choice. But both Byrne and Swinton are in a relationship with other people. Additionally, Ms. Swinton has typically rejected the "love triangle" idea.
Sure all this makes for interesting writing, but that bit about her personal life may be more sensational than it is accurate.