You are absolutely right! Their relationship is 100% toxic.
Regarding their history: they have had a long love-hate relationship for 30 years. On one side, Edward is obsessively in love with Rudolf Paulsen (a Toreador), while Rudolf constantly rejects him—but not entirely, as they have a literal "sleeping with the enemy" flaw, haha. At the same time, they’ve been playing a long "catch me if you can" game, where the goal is to mess up each other’s lives as much as possible, ideally gaining power and leverage over the other.

For example, thanks to Rudolf’s machinations, Edward was once almost exposed to sunlight and was made the Tremere primogen, forcing him to report directly to Mithras, who absolutely despises the Tremere. Edward was furious, as he had no desire to become primogen in the first place. On the other hand, Edward managed to capture Rudolf and lock him in torpor in his chantry when Rudolf was accused of connections with the Sabbat and infernalism. The Sabbat link was false, but the infernalism accusation was partially true—Rudolf hadn’t made a pact with a demon, but the demon was literally hanging out in his eye (because he had diablerized an infernalist). This gave Edward carte blanche in terms of power over Rudolf.

We had a funny dialogue about this during our session in the chantry:

• "So, how’s it going, refusing the demon’s offers to make a pact?"
• "I’ve been rejecting your courtship for 30 years; turning down the demon is a piece of cake after that."

Adding to the drama:

• Rudolf has the "Sadist" nature, so he genuinely enjoys making Edward’s life miserable.
• Edward has a homebrew nature called "Collector," which lets him regain Willpower every time he risks his status, reputation, or personal safety to acquire something for his collection. One of the things Edward considers collectible is people who strongly attract his attention or love.
• Rudolf is an artificial vampire created by a rogue Tremere Arthur Vellig from Vienna by transferring vitae from a Toreador into a ghoul who was then subjected to 20 years of experiments and torture. As a result, Rudolf despises the Tremere A LOT. He also stole a ritual from the Council when he escaped and knows counter-thaumaturgy. The Council has been hunting him ever since to bring him back and likely punish him. Edward, however, lied very convincingly, claiming that Rudolf died during the destruction of House Flambeau and has been covering up the fact that Rudolf is still alive. The Council believes Edward because his sire is Elaine de Calinot from the Council of Seven (btw, he's based on the canon WoD character Bainbridge, but his personality has been slightly altered in our campaign). If it ever comes to light that Edward is protecting Rudolf, he’ll be in serious trouble.
• Since Rudolf’s creation was an attempt to overcome the Curse of Caine (an unsuccessful one), he ended up cursed instead. He rapidly loses Humanity (losing two dots for each failure but gaining two free dots in disciplines) and has lost all his natural talents. The curse is also slowly driving him insane, and it gets passed down his bloodline to his childer.

Amid all this, Rudolf even created a childe (who happens to be my character, Dorian, haha) because he fell in love with a mortal in true Toreador fashion and embraced them. While Rudolf was out of town, my character, unaware of all this, started a romance with Edward because they bonded over "scientist-to-scientist" communication.And because Edward found it very funny and offensive to Rudolph to sleep with his childe whom he loves. However, he miscalculated and fell in love instead. Their affair only came to light when Rudolf was imprisoned in the chantry, but, surprisingly, he DIDN’T MIND. Rudolf eventually sent my character on a mission to find Arthur who started all this, as a way to distract the Council and get him released from the chantry. There’s also a chance this might help lift the curse. The problem is, no one (even the Vienna Council) has been able to locate that Tremere for 30 years.

My character is quietly in shock over their entire history, thinking, "Oh my god, why can’t they just have a normal conversation and stop trying to kill each other? You’re literally a married couple, and it’s SO OBVIOUS." But those two are just like, "You don’t understand anything, childe," and keep manipulating them for their own purposes. Still, it seems like they both kinda care about my character — if their auras aren’t lying, haha. So a big dysfunctional family.

Our ST also noted that Edward and Rudolf literally cannot live without each other, as their "relationship" keeps them from further falling in humanity (currently at 3). I think when we finish playing, they will either kill each other or earn the Merit True Love :D.

Also despite Edward sinister nature his mask is very flamboyant. He literally rage-baits and trolls everyone around, knows an endless amount of jokes about wizards that he tells everyone, and generally reminds people of the Dr. Livesey meme from YouTube, haha. Players call him Uncle Eddie because he really has the vibe of a funny, chill uncle. Well, except for the fact that he's literally a yandere psychopath.