Helga is sorely tempted to kill Irene and has a massive internal war between securing Jim for herself and not committing murder. She eventually realizes that if Irene dies and Jim finds out, he'll hate her forever and she won't have him anyway, so she decides not to kill Irene.
Helga doesn't swing that way, and still tries to kill Irene because she's still a potential threat to a Helga-Jim pairing (and no one considers Polyamory viable).
After another strong temptation to slash Irene's throat, Helga realizes she's going to lose eventually to the urge to kill. She resolves to remove the hypotenuse once and for all - herself.
Helga is all sweetness and smiles when Jim is looking, but keeps lunging for Irene with a knife the instant Jim turns his back.
Alternatively, Helga still lunges at Irene when Jim is looking, but she's lunging at her with a rubber inflatable sword that squeaks every time it hits. Because of this, Irene and Jim think that Helga is just kidding around and have a laugh about it.
Zig Zagged: Helga poisons Irene's drink, but then has second thoughts and tries to get the drink back, causing hilarity to ensue as they play Poisoned Chalice Switcheroo. They are interrupted when Jim enters the room and takes a sip from the drink himself, which is Played for Drama. It turns out, though, that you need to drink more than a sip for the poison to be noticeable, and Jim starts asking why Helga looked so upset. Helga, overreacting and failing to think of an excuse, drinks the whole thing herself while declaring "You'll never take me alive!"
Averted: Helga resolves to win Jim's heart by fair means.
Enforced: The writers want Helga out of the story, and having her get arrested for derailing herself seems the quickest way.
Lampshaded: "Did you see the look on Helga's face? I bet Irene is checking her drinks pretty damn carefully these days."
Invoked: Helga is encouraged to kill Irene by someone else who wants her dead.
Exploited: Helga tries to kill Irene, but Irene knew it was going to happen; so, she sets a trap in order to expose her true face to everyone else, including Jim.
Defied: Helga deliberately avoids Jim and Irene so that she won't be tempted to do something she'd regret.
Discussed: "She should have been your first suspect. The jealous lover is one of the oldest ones in the book, aside from the Butler, of course."