Chapter 9 is probably the best place to look for the answer to this question.

"Angela and I are going together; we're partners, you know." Sydelle had it all planned. They were to appear in identical costumes; tonight was the night they would discover if one of the heirs was a twin.

Sydelle wants Angela and her to dress as twins because she believes that dressing up as twins will somehow miraculously allow her discover which of the potential heirs has a twin.

Sydelle got stuck on the twin idea in chapter 8. When the rules of the Westing Game were given to the players, the object of the game was listed as "to win." In chapter 8, one of the other players realizes that "to win" sounds very similar to "twin," and the person comments that the object of the game might not be to win but to find the twin.

Sydelle really likes that idea and believes there is a lot of potential truth with that line of thinking, and she begins brainstorming on ways to have the murderer admit he or she is a twin. This is why Sydelle wants Angela and her to dress as twins when they attend the party. Sydelle believes that her twin costume plan will easily get people talking about twins, and hopefully someone will admit that he or she is a twin. The plan is foiled when Angela's mother makes her change, but Sydelle carries on and tries to steer conversations in the direction of twins.