The Scriptures tell us how various family relations crimes should be punished (all verse references are to Leviticus 20):
Cursing Mother or Father - Death (9)
For every one that curseth his father or his mother shall be surely put to death: he hath cursed his father or his mother; his blood shall be upon him.
Adulterer and Adulteress - Death (10)
And the man that committeth adultery with another man's wife, even he that committeth adultery with his neighbour's wife, the adulterer and the adulteress shall surely be put to death.
Incest with Father's Wife - Death (11)
And the man that lieth with his father's wife hath uncovered his father's nakedness: both of them shall surely be put to death; their blood shall be upon them.
Incest with Daughter in Law - Death (12)
And if a man lie with his daughter in law, both of them shall surely be put to death: they have wrought confusion; their blood shall be upon them.
Male Homosexuality - Death (13)
If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: they shall surely be put to death; their blood shall be upon them.
Incest with Step-Daughter, Daughter, or Mother-in-Law - Death by Fire (14)
And if a man take a wife and her mother, it is wickedness: they shall be burnt with fire, both he and they; that there be no wickedness among you.
Male or Female Bestiality - Death (15-16)
And if a man lie with a beast, he shall surely be put to death: and ye shall slay the beast. And if a woman approach unto any beast, and lie down thereto, thou shalt kill the woman, and the beast: they shall surely be put to death; their blood shall be upon them.
Incest with Sister or Half-Sister - God Will Punish (17)
And if a man shall take his sister, his father's daughter, or his mother's daughter, and see her nakedness, and she see his nakedness; it is a wicked thing; and they shall be cut off in the sight of their people: he hath uncovered his sister's nakedness; he shall bear his iniquity.
Sex During a Woman's Period - God Will Punish (18)
And if a man shall lie with a woman having her sickness, and shall uncover her nakedness; he hath discovered her fountain, and she hath uncovered the fountain of her blood: and both of them shall be cut off from among their people.
Incest with Aunt - God Will Punish (19-20)
And thou shalt not uncover the nakedness of thy mother's sister, nor of thy father's sister: for he uncovereth his near kin: they shall bear their iniquity. And if a man shall lie with his uncle's wife, he hath uncovered his uncle's nakedness: they shall bear their sin; they shall die childless.
Incest with Sister-in-Law - God Will Punish (21)
And if a man shall take his brother's wife, it is an unclean thing: he hath uncovered his brother's nakedness; they shall be childless.
Yes, male homosexuality is set forth as being a capital crime, like a number of family relations crimes. In terms of the sentence given it, it is more heinous in God's sight than certain kinds of incest and period violation. But for those of you who like to beat up on homosexuals, note that it is not the most heinous. The most heinous is taking both a woman and her mother. There, the punishment is not just death, but death by fire.
So, no. The appropriate Biblical teaching regarding how to deal with these family crimes is not internment in a prison camp.
On the other hand, if you want to rush to impose the Biblical sentence of death, keep in mind that for consistency you must be ready to hand out death sentences for bestiality, all adulterers, and most types of incest. You also can't include lesbians in your plan. While Scripture certainly does teach that lesbianism is a sin, the code doesn't provide for lesbianism to be punished.