Hello!

First I'm gonna set the occupation matters straight, to make sure no one gets confuses. Iceland wasn't occupied by Germany, but by the UK for one year and afterwards the US. When you refer to "after the German occupation was over", I'm assuming you mean the occupation of Denmark.

Denmark didn't try to reestablish control of Iceland, as they in fact didn't have legal backing for controlling Iceland anymore.

In 1918 Denmark an Iceland agreed to the Danish–Icelandic Act of Union, where they were in a personal union and Iceland was thus accepted as a sovereign state. This union was limited to 25 years. As a part of this union, Iceland asked Denmark to represent them in foreign policy. Denmark didn't have anything to say in regards to Iceland's domestic policies.

When they established this act, they also made a law with a stipulation, that both parts of the agreement could ask for a review in 1940 and if an agreement haven't been reached within 3 years, each part could unilaterally revoke the union. As we alle know WWII happened in 1940 and Iceland's parliament decided to overtake their foreign affairs from Denmark, now that they weren't able to undertake their obligations as part of the agreement. When the agreement expired on 31st of December 1943, Island decided to hold a referendum on whether or not to prolong the union, in which they overwhelmingly voted to become a fully independent republic. Denmark wanted to continue the union, but not against Iceland's will.

Denmark formally repealed their part of the union act in 1950, after they had come to an agreement with Iceland about the two countries future relations.

TLDR: Denmark didn't try to reestablish control over Iceland for two reasons. 1: After 1918 Denmark only had control over Iceland's foreign affairs, and thus no say in domestic affairs. 2: According to the union act Iceland was by the end of 1943 an independent country, because the time frame had run out without any new agreements on the union and because the Icelandic people in may 1944 had lawfully voted for their independence.

They are in Danish, but the Act of Union can be read here and the law where Denmark repealed the Act of union can be seen here.

I hope you find my answer fulfilling!