Constitutionally, the Queen can only act on the advice of her ministers. Her ministers, in turn. must command the support of a majority of the House of Commons in order to form a government.
The Royal Veto, while it exists in theory, hasn’t been used since 1708.
If you don’t like what happened in Rhodesia, at minimum you would need to blame Margaret Thatcher, who in turn was trying to clean up a mess handed to her by Ian Smith, Harold Wilson, Edward Heath, and James Callaghan.
The one person you can’t blame for that situation is the Queen.
Was the queen vocal about Rhodesia (and South Africa) or not? Did she take position ahead of Thatcher or not? If she did, Queen Elizabeth II pushed Thatcher, not the other way around.