I wouldn't train in the US if I were you. There are many reasons which support my answer to your question.
Firstly, the FAA license is too easy. It is of equal difficulty as getting a PPL in Europe. As the EASA license is more difficult to obtain, I suggest taking the hard route first before considering any conversions to an FAA license, an easier license to obtain.
Secondly, I hear the airline industry in America isn't doing too well at the moment, with jobs being hard to find, and with pay being very poor. Morale is not a strong point for pilots over in America either.
Thirdly, it is much easier to convert an EASA license to an FAA license (referring back to my first point).
And Finally, the standard of living is much better in Europe than it is in America. You'd be better off getting a job in Europe and living here rather than in America.
Nevertheless, this is all down to you. Maybe you'd like to live close to your sister. I'm just giving you advice.
TheSkiingPilot