I must honestly say, I don't have the skill or knowledge to be able to judge Mourinho correctly. In my opinion, it would be better to part ways, because even if it is just confidence that you need, isn't that part of the jobdescription for a coach as well?
Whenever I find myself in such situations though, when my knowledge is not enough, I just refer to the following tool: I just watch the results.
Mourinho is with your for a long time now and if you want him or not boils down to three simple questions:
1. Were the results sufficient? Were you happy with the results?
2. Did you like and enjoy the entertainment that you have seen?
3. What about the players in your team? Did your coach make them confident, strong and in the end of the day, better players? Did he pick the right players to strengthen your squad?
If all questions are answered with a "no", it is safe to say that the coach and the team should part or you should re-think your expectations. Because it can very well be possible that they are too high. The PL is a very, very contested league, this is the reason why we from the other countries watch closely. So it can always happen that you are not a part of the top 4. And if expecations are high and you are unhappy with your team and your players, it can always lead to frustration, which will in the very end, catch up with your team as well.
The integral things to successfull football are the following:
1. the players need to have fun playing, it should be visible that they love their team and the game
2. you obviously need above average players with a few exceptional ones that carry the team
3. the leading management, coach, director or however you call it in English, they need to have a vision, an identity
4. the supporters make their team stronger by supporting, not by criticising and whistling (not that you guys do that, just a general idea, even though it is safe to say that supporters are unhappy with the club right now)
From an outside perspective, I think that your players are good enough, not on all positions, but with your side, you should be able to reach your goals. I agree that the players seem insecure.
What I miss the most and forgive me for my openness, because I really think that Manchester United is an amazing club, is an identity and a vision. You buy great players, but do those players fit into the style that you want to see? I sometimes have the feeling that you just buy players, because they are hot at the moment. Sometimes having much money can actually be a burden. Because you can just pour out money and you don't look for what you really need.
I might be very wrong here, because I don't watch your games every matchday and it is just from my subjective perspective. But it seems to me that exchanging the coach might not be enough, maybe the club needs to have a look at the management above Mourinho.