What does "I'll loose my daughter to him" mean?

He will ensure his daughter will be there to meet Hamlet while they oversee from behind the curtain.

Thank you.

I wonder if there is any intention of sex trade there, because some translators here say so.

Good lord Ori...
How many European families, or Princes were involved with the sex trade in the 14th ish Century? How many fathers would do that to their daughters???

It means he'll set his daughter loose on him. Or like a dog, sick 'em, send her to him and see what happens.

Like a dog? Is it an insult to his daughter?

No, I didn't mean to be insulting, I like dogs. Dogs are loyal. When you set a dog loose on someone or thing, they will show great determination to defend their master or bring back the hunt's bounty (ball).
A sailer lets loose the sails to catch the wind. He could catch a breeze or be dead in the water.
Generally if you let something loose, you give up control and are forced to see what the consequences are. By setting a dog or you daughter loose on someone, you know you can generally trust that they have your best interests at heart and you can imagine what they might do, but what they uncover remains to be seen. The outcome is uncertain.

I'm not at all sure that this is the modern, "turn someone/something loose on somebody, Ceili. The preposition used was 'to', not 'on'.

This is the language of the stable. Polonius treats Ophelia like a breeding mare, "loosing" (releasing) her to Hamlet as a horse breeder releases a mare to a stallion when mating the two animals. Later Hamlet calls Polonius a "fishmonger”, Elizabethan slang for “fleshmonger” - a pimp. In Hamlet’s view, Polonius treats Ophelia as so much flesh for barter– as if she is a mare for the breeding. But Polonius is even less honest than a pimp; he manipulates Ophelia for political capital, not just money.

It depends what you mean by the sex trade. The children of kings and princes weren't turning tricks on the street, but they were forced into marriages for political gain. This only changed very recently. George IV's marriage to Princess Caroline of Brunswick was particularly loveless.

Apparently it means that he will lose his daughter to someone, meaning the daughter will marry or go away with that other person and will no longer be close to the father. It seems Shakespeare used to write "loose" instead of "lose" (Oxford Dict. Unabridged):

4.4 absol. or intr. a.4.a To suffer loss; to cease to possess something; to be deprived of or part with some of his or its possessions, attributes, or qualities; to become deteriorated or incur disadvantage.

   c 1230 Hali Meid. 41 Ha beon eauer feard for to losen [elsewhere, and here in MS. Bodl. leosen].    c 1470 Henry Wallace iv. 336 Now want, now has; now loss, now can wyn.    1596 Shakes. Tam. Shr. Induct. ii. 101 Thou shalt not loose by it.    1611 Bible Eccl. iii. 6 A time to get, and a time to lose.    1643 J. Burroughes Exp. Hosea iv. (1652) 75 There is nothing lost in being willing to lose for God.    1697 Dryden Ded. Æneis Ess. (ed. Ker) II. 229 Thus, by gaining abroad, he lost at home.    1838 Macaulay Temple Ess. (1887) 440 He never put himself prominently before the public eye, except at conjunctures when he was almost certain to gain and could not possibly lose.    1850 Tennyson In Mem. xxvii, 'Tis better to have loved and lost Than never to have loved at all.    1895 George Battles Eng. Hist. 313 Fortunately the Sikhs had lost so severely that no evil consequences followed.    1898 Folk-Lore Sept. 198 The other was undertaken by a publisher, who lost on it.    Mod. Both armies lost heavily.

It definitely does not mean that. I suspect you have become yet another victim of the all-too-common lose/loose confusion that so many people suffer from, or else you have found stuff on the web put there by sufferers and have imbibed it uncritically.

I can live with the accusation that it may not mean that. What I cannot live with is the accusation that I have become yet another victim yada yada. Have you not seen the bit I posted from the Oxford Dictionary and how Shakespeare wrote "lose"?

Shakespeare often spelled the same words differently in different places, sometimes within the same play. If there were any doubt, the context of the line makes clear what Shakespeare meant by "loose" in this particular place.