It's actually quite likely that Nobunaga didn't call Hideyoshi "monkey". While a lot of descriptions of Hideyoshi wrote that he looked like a monkey, I am not aware of any narrative sources that says anyone actually called him monkey. The one letter where a "Monkey" was mentioned actually have a high probability of not referring to Hideyoshi, instead to an unknown aide who's name was "Monkey", which is not weird as we're told of other aides who's names were "Rock" and "Bear". Of course it could actually be refering to Hideyoshi, it's debated.

We are sure Nobunaga did call Hideyoshi "bald rat" once. That's in the letter to Hideyoshi's wife, which said (according to my crappy Japanese level and translation):

I am delighted that you came here [to Azuchi Castle] and visited me as I asked. And you brought lots of gifts that are so beautiful I can't write down words to describe them. I thought I'd also give you something as thanks, but I can't think of anything on hand that are better than your gifts, so I won't this time. Next time you come, I'll give you gifts.
Your beauty have went from a 10 to a 20 since the last time I saw you. Tōkichirō [Hideyoshi] often say you're not enough, but that's preposterous. It's inexcusable. No matter where that bald rat look, he won't find as good a woman as you.
From now on, act as a good, proud wife, and do not be jealous. However, it is not the place of the wife to say whatever she wishes, but she should hold back some.
Also, ask Hashiba [Hideyoshi] for his opinion regarding this letter.
Regards
Nobu[naga] (Tenka Fubu seal)
To Tōkichirō [Hideyoshi] and lady

I don't know of any other example of a lord going this far in stepping into such personal matter, what seems to amount to a couple's quarrel, of his subordinates. It must be freaking rare. So contrary to popular depiction of Nobunaga treating his subordinates with coldness and disdain, he seems to have gone out of his way to look out for them, even if he used rough language. If not to everyone, at the very least, he seem to have taken great care of Hideyoshi and wife.

On the other hand, was his language all that rough? He addresses Hideyoshi properly multiple times in the letter. The one time he used "bald rat" was he voicing his disapproval at Hideyoshi badmouthing his wife. In context it does not seem particularly unreasonable.

It would be more unreasonable if he called Hideyoshi "bald rat" or "monkey" all the time, but we have no evidence of that. My translation of Luis Frois says that Nobunaga called almost everyone 貴様. I don't know if that's what Frois actually wrote, a form of "you" which would be considered close, friendly, and polite in the Sengoku, or if the translator picked the modern Japanese equivalent of what Frois wrote in Portuguese, which would be disrespectful. But Frois certainly didn't say Nobunaga called Hideyoshi "monkey".

Frois says Nobunaga "rarely if ever follows the advice of his retainers". But he also says Nobunaga "in conversation hates delays and circumlocution, and talks friendly with the lowest servant", and is "well respected by all". The picture Frois paints is not a cold, cruel man, but a rough, proud, confident (maybe a bit arrogant and narcissistic), straightforward, yet caring and charismatic man. Whether or not Nobunaga actually called Hideyoshi "bald rat" and/or "monkey" regularly, I don't think there's any evidence of unusual mistreatment or disdain.