No, Bryndhildr marry Sigurd (not Siegfried, thats the name for the German ver) after he saved ger from flaming stone bed. Because he is a warrior, one day, he got called by the kingdom and the princess of the kingdom fall in love upon meeting him. He is already married to Brynhildr so he refuse her approaches. When the princess consult the queen, her mother, she give her a potion that force amnesia. Sigurd later drink it when it's mixed with his meal during his stay in the kingdom. He forgot about himself and Bryndhildr and the princess, Gudrun then seduce him and he falls in love with her.
Brynhildr and her daughter with Siegfried waiting for him but never come back. One day, the king of the kingdom who is the brother of Gudrun, Gunnar saw Brynhildr searching for Sigurd and he likes her. He tries to seduce her but she said only the man that can save her from a flaming bed may become her husband. Sigurd offers his help to make Brynhildr marry Gunnar, which the king accept. Sigurd then disguise himself as Gunnar and saved Bryndhildr from the flaming bed...Again. It was said that his memory returns during this time but he was already married with Gudrun and have child with her, alongside his vow to help Gunnar, makes him reluctant to take Brynhildr back.
The one the other anon is saying is about Siegfried, Kriemhilld, Brunhilda, and Gunther. Which have different settings altogether but similar plot.
In addition, Lilith was said to be the first wife of Adam who refuse to be submissive to him and they seperates, where God later give Adam his second wife, Eve. Thats not Cuckqueaning. Yeah Brynhildr is more cuckqueaned in the story.