So one of the problems that Trump ran into in his first Administration was that he wanted his agencies to implement his policies really fast. Unfortunately, because government is not like a private business, that's not always possible. The federal government is constrained by the Administrative Procedure Act, which requires agencies to actually evaluate their policies and justify them with reasons other than "the CEO wants to do this." There's no substantive limits imposed by the APA, but it does require that process. For whatever reason, Trump's agencies didn't engage in that process (either because some of them were headed by people new to the federal government, or because they responded to directions to move more quickly than the APA allowed) - and Trump had a bunch of things tossed by the courts.

His weird demand on recess appointments shows that he hasn't quite learned his lesson. The SCOTUS decision in Canning, which held that Congress' pro forma sessions were sufficient to keep the recess appointment power from being triggered, was very hostile to the recess appointment power in the modern era. The Court's discussion made it clear that they were taking a pretty operational approach to interpreting the Clause - it's intended to make sure that when Congress cannot consider an appointment, the position can be filled so that there isn't a vacancy. It balances the Constitution's very clear role for the Senate against the practicalities that sometimes the Congress just isn't around, at least back in the days before air travel. But because short recesses don't present that problem (Congress will be back soon to take up the nomination in due course), anything less than ten days is presumptively too short to trigger the power.

Going out and asking the Senate Majority Leader to deliberately call a recess in order to sidestep the Advice and Consent Clause therefore seems....phenomenally short-sighted? If one of his nominations gets blocked/can't pass through the normal Senate process, and Thune calls a 12-day recess (just to pick a number), it seems somewhat unlikely that the courts will find the recess appointment to be legal. Every action taken by that person - possibly including firing the people that Trump wants fired - will be subject to challenge, just like in Canning, on the grounds that they weren't lawfully appointed to the position.