There was a lot of fighting going on and it was a miracle these movies were made. We didn't even discuss the Doohan,Takei and Roddenberry issues either.
I disagree there was "a lot of fighting". Mostly, it was agents posturing for better deals for actors who had
stopped getting residuals on their work after the third repeat on TV. Compared to actors starting out in TV in the 80s, the actors from TOS were way behind the eight ball. Overexposed and typecast, but not getting any residuals either. For some, convention appearances had become their only source of employment.
The biggest problem with Nimoy was "Phase II" (he refused to be involved). He was also getting plenty of work and didn't "need" ST. Robert Wise insisted that Paramount do everything in their power to tempt him back for ST:TMP. Problem solved. Nimoy was supposedly very happy with his TMP contract. Nimoy had his own disagreements with Gene Roddenberry over the years, but they buried that hatchet.
Nimoy didn't refuse to be involved in ST II for too long; but when it seemed he needed extra persuasion, Meyer and Bennett appealed to his acting chops; the idea of playing Spock's death scene was too much to resist.
The Doohan/Shatner feud was never seen on the soundstage, only ever in Doohan's convention shtick in his later years, thus it never threatened future ST films. Showing what a great actor Doohan was, there is
no sign in the ST movies - not even in "Generations", which was filmed
after Shatner found out how hated he was by the others - that Shatner and Doohan didn't get along. Scotty is quite affectionate of Kirk, esp. in TMP and "Generations". Shatner didn't socialize with any of the cast. He never showed up to their star ceremonies. He never really noticed they were annoyed by his "star" antics until they all began their autobiographies.
Ditto Takei. The ongoing Takei/Shatner feud was rarely seen on the soundstage, usually played for laughs, and was made public only in Takei's convention shtick, so it never threatened future films. Takei almost didn't sign for ST II, but it wasn't due to Shatner. But then Shatner supposedly spoiled the "Captain Sulu" promotion scene in that film, the bait that Bennett had used to lure Takei to sign up.