In some respects, part of the reason why Eliezer's family rejects the offer made from Martha could have been due to underestimating or not anticipating the horror that lies ahead. Many of those who refused such offers during the Holocaust did so out of denial, the perception that things could not really be as bad as believed. In part, it is the same reason why the Jewish people of Sighet refused to believe Moshe the Beadle and invalidated his own experiences. If a letter would be written to Eliezer's family in persuading them to accept Martha's offer, there are a couple of approaches which could be taken. One might be to simply implore Eliezer's father to save his family by accepting Martha's offer. This could be done with a tone that stresses "bad things" that lie ahead. Another could be to open your letter with those bad things. Perhaps this opening could be to relay the sights Eliezer saw in his experience at the Birkenau camps of children and babies being burned alive and the smoke from the burning of bodies. I think that in imploring the family to accept Martha's offer, your letter has to stress that they have little conception of how bad things will be and to take Martha's offer now might delay the witnessing of these events later.
During the time of the Third Reich the Jewish people could not accept nor really understand that a country or group of people could allow other people to be treated so badly. Many Jewish families under-estimated the power and the cruelty that the Nazis would undertake to delete the population of Jewish people.
Another important reason for not going into hiding was because the family of Wiesel were law abiding citizens. They knew they had done nothing wrong and falsely believed that at some point the government would protect them as citizens. They also did not feel that the morale was that bad at the Ghetto which gave them a false sense of security.
Martha begged Mr. Wiesel to go with him to her village for safekeeping, but he refused. He told Elie and his older sister that they could go with Martha but he would not. Elie and his sister decided to stay and keep the family together.