You are probably right that P. Roy was unbearable to work with as Coach/GM but he was not fired; he quit.
Tiga is right, Roy quit because he didn't have input into choosing his players - discussed in this Denver Post article:
http://www.denverpost.com/2016/08/11/patrick-roy-out-colorado-avalanche-coach/
To understand the true dynamics of Coach-GM relationships in the NHL, I recommend reading Phil Esposito's book "Thunder and Lightning", and in particular pages 191-202, which are devoted to discussing his relationship with former NY Rangers coach Michel Bergeron, whom Esposito rips as constantly meddling in and second guessing player personnel decisions. For one thing, Esposito was infuriated when Bergeron announced to the press he would no longer play Esposito acquisition John Ogrodnick- a player Bergeron wanted Esposito to get. This open GM criticism is similar to what Roy did at his press conference in April, discussed in the Post Article, in which he noted the lack of draft choices was hurting the Avalanche badly.
When Esposito fired back at Bergeron in the press that if the team did not win it was on Bergeron, Bergeron came with his agent to talk to Espo. Here is what Espo says about that on page 194:"When he came to see me, he brought his agent with him. I said, "are you kidding me? I got to deal with an agent - for a coach? I threw the agent out". "Listen", I told Michel, "coach the team and shut the fuck up!" Those were my exact words. "You make me laugh. I let you pick the players and decide who you're going to play. I don't tell you who to play. But if you're wrong, you're responsible for our not winning."
Also on page 194, Esposito said Bergeron told him to acquire Michel Goulet. Here is what he says:"Bergeron said to me, he could take the place of everybody on this godddamn team." Esposito told Bergeron that he couldn't acquire Goulet because he was too expensive to trade for.
On page 196, Espo discusses Bergeron refusing to play Don Maloney and this: "Bergy, meanwhile, kept bugging me to get him a big center." So Esposito traded Don Maloney for Carey Wilson to pacify Bergeron.
Next, they fought about what to do with the aging Marcel Dionne, who was slow to recover from an injury. On page 197: "Bergy didn't want him on the team any more. He would tell me to get rid of him. I'd say, Marcel stays for as long as he wants."
On page 198, Esposito accuses Bergeron of succumbing to the pressure of coaching in NYC, a pressure Bergeron created by constantly talking to the press behind Espo's back. According to Espo, due to the pressure, Bergeron developed coffee and smoking addictions.
The last straw was when the Rangers went into a losing streak and Bergeron told the press that Espo should have acquired Michel Goulet. Esposito informed Rangers President Jack Miller of his decision to fire Bergeron and offered to coach the team. Miller agreed and raised Esposito's salary from $400,000 to $500,000. Espo described the firing of Bergeron on page 201:
"I am making a change."
"A change in what?"
"In coaching," I said. "I am replacing you. Right now. I warned you twice not to go behind my back. The first time I told you if you did it againn you would be fired. The second time you did it they would not let me fire you. But when you did it the third time, three strikes and you're out."
"Are you crazy!" he said. "You can't do that. What's the matter with you, Phil?" He then asked, "who is going to coach?"
"I am."
"Oh yeah, you're going to coach," he said with great sarcasm. "Good luck."
Esposito repeatedly accuses Bergeron of inappopriate bias/favoritism towards French-speaking players and Assistant Coaches and Esposito told Bergeron all his French speaking assistants were also being fired. It is clear that this bias deeply disturbed Esposito.
This is the reality of Coach/GM relationships in the NHL. So this fantasy that Coaches do not have input in player personnel decisions and keep their mouths shot dutifully at all times is just that, a fantasy.