The key to understanding the sukebind is not how the Starkadders and their neighbours comment on its effects in the beginning of the novel, but in when it is removed or destroyed in the end of the novel.
When Elfie returned from Dick's birthday dance, and Aunt Ada finally saw that her family was defying her power over them,
...the heat of the fire had caused the long, pink buds of the sukebind to burst; the wreath which hung round the portrait of Fig Starkadder was covered with large flowers whose petals sprang back, like snarling fangs, to show the shameless heart that sent out full gusts of sweetness. (Chapter XVI)
Ada Doom then threw a tantrum screeching "from her heart-roots" as the sukebind withered. She called Flora names and "struck at [Flora] with the ‘Milk Producers’ Weekly Bulletin and Cowkeepers’ Guide’",
a withered flower fell from the sukebind wreath into the coals. (Chapter XVI)
And the conflict was over.
The next we hear of the sukebind, Reuben tells Flora that his grandmother chose to have "all the pictures wreathed with that smelly sukebind," but Flora may take it down as he "niver wants to see a sprig of it again." (Chapter XX) And so Flora gets rid of it, and the wedding is entirely sukebindless.
The wedding guests are greeted by Aunt Ada Doom rising "from a chair wreathed in peonies" and then literally flies away, finding her own freedom just like the rest of her family did.
The sukebind is not sex, or animalistic urges. It is the oppression which hung over the Starkadder Farm preventing its inhabitants from finding their own joy. Instead each person sought sullen distractions from their predicament according to their character at the expense of others. As each person became able to seek their own joy, the sukebind burned, withered, and was thrown out. It is most directly associated with Aunt Doom, because her choice of distractions were the most harmful to those around her, and she clung to them the longest of all the Starkadders--seeking cold comfort in her familiar misery.