Sprinkle 1 envelope unflavored gelatin over 2 tablespoons water in a cup; let soften 5 minutes. Place cup in small pan of hot water, stirring until gelatin is dissolved. Stir in 1/3 cup light rum. Beat 2 cups heavy cream in a medium-sized bowl until soft peaks form. Beat in 1/2 cup 10X (confectioners') sugar and continue beating until stiff peaks form. (Do not overbeat.) Fold gelatin mixture into whipped cream.
Melt 4 squares unsweetened chocolate over hot, not boiling, water. Remove from heat; stir in 2 cups sifted 10X (confectioners') sugar, 2 tablespoons hot water and 6 tablespoons softened butter; beat with electric mixer until smooth. Beat in 2 eggs, one at a time. Place bowl in larger bowl of ice and water, and beat until mixture is thick enough to spread, about 10 minutes.