Dear Windmill,
Thanks again for requesting me.
Filing for the green card lottery will not affect your abiltiy to travel on visa waiver between the Neatherlands and the United States. You should have no encumberances while waiting for the results of the Lottery.
AN FYI: The way the lottery works, nearly everyone who applies is actually drawn. It is that the lottery assigns priority numbers in sequence of the draw. They first designated number of names drawn are given first opportunity to take advantage of applying for the green card. As people decline the opportunity, or thier opportunity expires, other names are moved up in the queue. They will stop drawing names at some predetermined point, but if all the names drawn were exhausted, then they would continue to draw until all green card "goals" by lottery are filled.
It would be quicker to pursue a work permit and then get green card sponsorship.
Of what status are your relatives in the U.S.
It is possible to allow an adoption or gaurdianship of your daughter by your relatives, and that they can bring her in to the U.S. as a family member. However this has to be a court orderd arrangement, even if you and the relative agree to the conditions and terms.
In an earlier question, I suggested a cultural exchange program, where she might attend as a J-1 visa.
I can search for a program for you.
What state, city, and school grade would your daughter be attending in the U.S.?
YOUR PAYMENT AND BONUS IF ANY MAY BE TAX DEDUCTIBLE

Edward M. Johnson