ВНИМАНИЕ: приведенный выше код выполняет вашу работу, но НЕ является эволюционным!
# I want to groupby ID excluding the line for 2012-10-11
df1 = df.loc[df.DATE != '2012-10-11']
# 1 - df1.groupby('ID').sum() -> I groupby ID to get the sum
# 2 - df1.drop('NUMBER', axis=1) -> I drop the col NUMBER to avoid overlaping columns
# 3 I merge the to df to get the sum value for every initial lines
df1 = df1.drop('NUMBER', axis=1).merge(df1.groupby('ID').sum(), on='ID')
# I get back the ligne for 2012-10-11
df1 = df1.append(df.loc[df.DATE == '2012-10-11'], sort=True)
df1 = df1.sort_values(['ID', 'DATE'])
# I delete the line I don't want
df1 = df1.loc[df1.DATE != '2012-10-13']
print(df1)