I have to agree with your husband that it will probably be difficult for you to pass a background investigation, even though you haven't done anything wrong.

To begin with, note that roughly half of FBI special agent applicants who make it past Phase I and Phase II testing are presently being accused of deception (many, and perhaps most, falsely) based on pseudoscientific polygraph results, which become a permanent government record. In my opinion, this is reason enough for anyone to avoid the FBI like the plague. See my article, Just Say 'No' to FBI Polygraphs.

Second, U.S. security officials are notoriously xenophobic. The fact that your father and sister work for the military of a foreign government will be of considerable concern, especially if you remain close to them. So, too, will the fact that you have only recently become a U.S. citizen. See  Security Clearances and National Security Information: Law and Procedures (17.5mb PDF) for more on how policies have been applied:

http://antipolygraph.org/documents/security-clearances.pdf

Finally, instead of inspiring admiration for your loyalty to your newly adopted country, the fact that you are willing to take a 50% pay cut to work for the FBI is likely to arouse deep suspicion on the part of background investigators.

I think you would be wise to keep your present job.

lala,

Sorry to dash your dreams, but I have to agree with George. Although your ambition is admirable, it is highly doubtful you would even make it to the poly with the FBI. Before applicants receive a conditional job offer, they must submit a completed backgound investigation form, which will reveal your relatives living overseas. Such a circumstance is a common reason for a security clearance denial in the FBI. I would imagine the agency would not even waste it's time by extending you a conditional job offer. There are other ways to become an investigator without working for the FBI. Perhaps, that's an option you could explore. Good luck to you.

Lala,

    If you want to be an investigator, you could always look into the local level or even the private sector.  Many people i know tell me I should seek employment with the FBI or some other federal agency in lieu of persuing it on the local level, which I am currrently doing.  I have no desire to work for the feds, especially after reading what I've read on this site alone.

-Smokey