AFAIK you apply to the country where you are entering the Schengen Area. Once in, you can travel freely to all other Schengen countries. Since there are no checks crossing intra-Schengen borders, nobody even knows which countries you have been in.
It is not necessary to return to the Netherlands to exit from the Schengen Area, you can return home direct from Italy, or any other Schengen country.
There is no "Netherlands Embassy in San Francisco,". There is only one Embassy in each country, usually in the capital city. The "branch offices", like the one in San Francisco, are called "consulates".
If still in doubt, ask the consulate when you apply.