Why did Elizabeth II refuse to accept the title of queen in Rhodesia when other nations such as Canada, Australia, New Zealand and South Africa remained under the monarchy with their independence?

Edit: Your question is unclear, but I'm going to answer what I think you were asking.

Elizabeth II was the head of state of the colony of Southern Rhodesia until UDI in 1965. The UK's policy at the time was "No independence before majority rule." That meant that for a British colony to become an independent member of the commonwealth they could no longer be under white minority rule, which was not something the Rhodesian government was interested in.

From UDI in 1965 until 1970 Rhodesia was legally a colony in rebellion. As far as the rest of the world was concerned the government there was illegal and illegitimate. That's why Elizabeth wasn't the head of state of the Rhodesian government, there was no legitimate government for her to be the queen of. In 1970 Rhodesia declared itself a republic and all pretense of loyalty to the crown was given up.

Interestingly, Elizabeth II did briefly become head of state again from late 1979 to early 1980. After the Lancaster House Agreement that ended the Rhodesian Bush War the country briefly became a colony of the UK again until elections could be held. During that time Elizabeth was the queen again.