Yes, odd he didn’t fire all political appointees like most previous presidents. But the union, that would get stopped in court before the ink dried (unlike New Mexico governor’s suspension of 2nd amendment that can’t get into a courtroom.)
True, in that everything Trump did was attacked in court.
He could attempt it in two parts, the first being, not allow the use of government facilities for union reps and not allowing OMB withhold union dues out of the paychecks.
Both of those would fall under the constitutional provision that government money is not to be used for private purposes.
He’d also have to act fast - firing anyone not making that happen for insubordination before a stay gets in place.
Then they can sue him for reinstating that and he can simply not participate, sort of like Andrew Jackson operated.