I have two adopted children. They are adopted from Peru and Ecuador. Both were converted via Orthodox Beth Din. Although both look `different` to their friends, they are very much accepted and nobody has cast doubt on their conversions or their Jewishness. They are now both young adults.
I think what sums it all up is what a Rabbi once said to me. He said that when all the children of Israel were gathered at Mount Sinai - even the souls of Jewish people not yet born were there, and this means that the souls of any Jew was there - especially that of a soul that was going to be converted to Judaism.
Our adopted childen that we converted ARE Jewish and always will be. Good luck to everyone.