I think it's very good that you are being put outside of your comfort zone--that is the only way we grow as humans. It is an integral part of Christian culture to greet each other with hugs and kisses. Without wanting to be overly judgmental, the idea that a family could never hug and kiss one another and would never express emotions seems foreign to the way that the Old Testament patriarchs, Christ, the Apostles, and Saints have shown us that humans are supposed to act (your family may be non-Christian, Protestant, or something else; I am not sure, so I am not sure where they are coming from). I would continue to put myself in this uncomfortable position until such time as it feels natural; because, as I said, this is an integral part of Orthodox culture.
My family started out reserved, although not to the extent you have said yours is, but we have gradually become more expressive and it feels liberating to be able to tell family that I love them and hear that they love me back. I don't expect that you will be able to impose this on them but for you, over time, you may come to appreciate the freedom to express yourself.
If you or any other reader has social anxiety issues though, please ignore what I have said and consult a professional as to your feelings as I am an unlicensed, untrained, and unsolicited-advice giving layman and would never want to give out advice that is not applicable or beyond reasonable limits.