Mr. Frank's Soldier's Box Question

I assume that the same 'better treatment' would have applied to his family also, but only because this was in keeping with the purpose of the Theresienstadt camp, which was used as a propaganda tool. There was no reason for the Nazis not to extend their invitation to include a veteran's whole family, as the decent treatment that was promised was a sham.

The camp served as a 'model' camp, and allowed the Nazi regime to maintain the illusion that Jewish detainees in camps were being relatively well treated. The cynicism that lay behind this is revealed by the fact that, prior to a Red Cross visit in 1944, many inhabitants were deported to Auschwitz to make the camp appear less overcrowded.

A propaganda film portraying conditions within the camp as being humane was also produced by Jewish director Kurt Gerron, an inmate there, allegedly on the promise that his life would be spared in return for his cooperation. Upon completion of the film he was also sent to Auschwitz, and immediately gassed upon arrival.

There were regular transports taking inmates from from Theresienstadt to extermination camps, serious overcrowding problems and, towards the end of the war, a further influx of inmates who had been evacuated from other camps further East as those areas fell to the advancing Russian army, and these inmates brought with them not only horror stories of the the extermination camps to the East, but epidemic typhus.

Ultimately only around 10% of the 144,000 Jews who were sent to the camp survived. There's no particular reason to think that the Franks would have fared better by turning themselves in right away compared to hiding for as long as they could.

I assume that Otto Frank was, rightly, sceptical about promises of well treatment, and thought his family stood a better chance of surviving by remaining hidden rather than placing any trust in the regime that had already driven the Franks from their native Germany. This must have seemed particularly so when the tide of war turned decisively against Germany.

He came agonisingly close to being correct, as if they had been caught only one month later, they would likely have survived the war at Westerbork Transit Camp. They were however caught in August 1944, after being in hiding for 25 months, and transported on the final prisoner transfer train from Westerbork to Auschwitz, which departed in September.