The use by three heavyweight European powers of information

  1. The use by three heavyweight European powers of information from secret services in countries that routinely rely on torture was damaging the reputation of the entire European Union, said the rights group.

  2. The use of information from secret services in countries that routinely rely on torture by three heavyweight European powers was damaging the reputation of the entire European Union, said the rights group.
    Can I rewrite #1 as #2?
    If it is possible, which one is better?

1 is correct.
2 places the ‘powers’ too near the ‘torture’ and so confuses matters. It looks as if the torture was being carries out by the European powers!