Solution

First, we have to modify the widget creation function to return a new column for the second option.

#We can expand this to allow for combinations of options too!
widget_box.close()

#Update the widget box
def create_widgets():
    #Create the two vertical boxes
    simulation_parameters_box = create_simulation_parameters_box()
    option_parameters_box1 = create_option_parameters_box()
    option_parameters_box2 = create_option_parameters_box()
    
    #Put them together with a horizontal box
    return HBox([simulation_parameters_box, option_parameters_box1, option_parameters_box2])
widget_box = create_widgets()
display(widget_box)

After this, we can also modify the actual valuation formula to include both options.

widget_box.close()

def valuation(S, sigma, rf, T, T_increment, X1, O1, Side1,
             X2, O2, Side2):
    #Set t_increment based on the qualitative choice
    if T_increment == "Trading Day":
        T_increment = 1/252
    elif T_increment == "Month":
        T_increment = 1/12
    elif T_increment == "Quarter":
        T_increment = 1/4
    elif T_increment == "Year":
        T_increment = 1
    else:
        assert False
    node_levels = create_nodes(S, T, sigma, T_increment)
    
    #Put in the strike price, and chose the option formula based on the input
    if O1 == "Call":
        opt_formula1 = call_value
    elif O1 == "Put":
        opt_formula1 = put_value
        
    if O2 == "Call":
        opt_formula2 = call_value
    elif O2 == "Put":
        opt_formula2 = put_value
        
    opt_values1 = backward_induction(node_levels, X1, sigma, rf, T_increment, opt_formula1)
    opt_values2 = backward_induction(node_levels, X2, sigma, rf, T_increment, opt_formula2)
    
    if Side1 == "Long":
        pass
    elif Side1 == "Short":
        opt_values1 = [-x for x in opt_values1]
    else:
        assert False
        
    if Side2 == "Long":
        pass
    elif Side2 == "Short":
        opt_values2 = [-x for x in opt_values2]
    else:
        assert False
        
    opt_values = [x+y for x,y in zip(opt_values1, opt_values2)]
    
    node_levels = convert_nodes_to_labels(node_levels)
    opt_labels = convert_nodes_to_labels(opt_values)
    
    pos_dictionary = create_node_positions(node_levels)
    print("Stock Values")
    draw_binary_tree(node_levels, pos_dictionary,node_levels)
    print("Option Combination Values")
    draw_binary_tree(node_levels, pos_dictionary,opt_labels)
    
    
widget_box = create_widgets()
output_object = interactive_output(valuation,{"S":widget_box.children[0].children[0],
                                             "sigma":widget_box.children[0].children[1],
                                             "rf":widget_box.children[0].children[2],
                                             "T":widget_box.children[0].children[3],
                                             "T_increment":widget_box.children[0].children[4],
                                             "X1": widget_box.children[1].children[0],
                                             "O1": widget_box.children[1].children[1],
                                             "Side1": widget_box.children[1].children[2],
                                             "X2": widget_box.children[2].children[0],
                                             "O2": widget_box.children[2].children[1],
                                             "Side2": widget_box.children[2].children[2]})
display(VBox([widget_box, output_object]))