Let me try a hypothetical on you for size. Suppose a judge somewhere decides he wants to rule on whether Donald Trump can have JD Vance as his Vice President on the grounds that JD may not be married to an American and thus this might constitutes a potential conflict of interests for the Country. Based on that claim the judge orders a temporary injunction barring JD as Vice President until the Judge is able to have a full hearing on the facts...
What would you say Trump's response should be?
It’s quite simple. Musk himself said it the other day: The courts cannot control the legitimate action of the Executive.
The important word is ‘legitimate’. The courts, however, have a duty to control the ILLEGITIMATE actions of the executive. There are three co-equal parts of the constitution. If one part becomes dominant, the checks and balances cease to exist.
Now (Leaving aside for the minute the issue of a temporary injunction) the question in your example is: what law or constitutional provision makes lawful a decision of a judge to estopp the appointment of Vance as VP? In giving such a ruling the judge is required to apply a law to the facts and give his reasoning in a written judgement. If he is wrong, the correct response is to appeal. The judge may not apply a fictional law, simply because he does not approve personally of events.
While waiting for the appeal, the judgement must be obeyed.
A temporary stay makes no difference other than the judge is signalling that there arguments on both sides which which need airing at a full hearing. So, if there is a law or constitutional provision which MAY enable the appointment to be estopped, the judge will raise that question while issuing the temporary stay.
You forget an important point in your eg. A judge will not unilaterally decide something, there has to be a party raising the question through an application to the court. If an organisation were to make an application, it must give the legal grounds upon which the application is based. The judge would rule out the case immediately if there were no legal grounds.