mix personal angst into professional conduct

I am not here to correct individual behavior or their personal lifestyle. I am here for a purpose and that is to maintain a healthy team culture in which everyone participates and contributes professionally towards meeting team/group goals.
Everyone has personal needs but they should be able to contain them and sort it out personally either through direct interactions or escalations but should not disturb team's environment to further their cause. They should display a maturity in professional conduct and should not corrupt it for personal needs.
I would have left this issue here if the person in question would have been satisfied by giving me negative 360 but I found that the venom has been passed on to the team too and therefore I am providing this recommendation.
He could not adopt to the ambiguous work environment that comes with a solution setup that is happening for the first time. He could not learn what all we were doing and still will show no interest. He was only focused for the task at hand and showed no interest towards various initiatives that I took for team's welfare. He maintained his own timing and did not bother whether it affected team's need or not. He misused company's resources like Cab for personal reasons like cricket match. He cannot pick up new areas of work quickly and takes too much time to adopt to newer technology. He is not able to generate respect in a team of freshers. He is reluctant to ask for help from his teammates and even after being told that there is a teammate who has done so and so and why don't you discuss the same with him and resolve. He demands respect for his years of experience. His suggestions are silly and diverts team attention and directions and thus get ignored like shift meeting from 10 to 10:05. His explanations are silly and non-consistent like sometimes he mentions that he had backache 3 months back so came at 12 today or yesterday he slept at 12 and so he came at 12 today.

I would have still accommodated him but he has been a difficult resource in course of this project.
At the start of the project I had mentioned that he is lead designer for this project and thus all ideas should be filtered by him and should pass on to team only after he had done its impact analysis on coding/testing etc., He said I was not able to communicate the delay so I was not accepting any changes.
The design of his module went on for endless discussions even after I repeated that start putting it on paper so that I can review the progress and finally when it came on paper the coders were uncomfortable because there was no detail to carry forward to code. On one Friday they came to me and I had to ask them to define the design by themselves and go ahead, there was already a delay of 1 week and no more delays could be tolerated by the schedule. The coders defined the designed on paper and even then the final design documentation is very poor.
During the design phase on Friday evening he tells me that he is on training on Monday. I try to persuade him to understand that a delay in design will have severe impact on coding and thus the whole project. He tells me that he will decide on Monday. I go to the coder and tell him that understand the design verbally and go ahead with your coding because I would not know when it will come out on paper. This is after repeated reminder that his design is a dependency.He finally skipped the training.
I had made a mandate in the team that we should restrain from taking leave as it was a critical target driven project for us and we should all finish our as well as help teammates to finish their task earlier. He comes to me on Wednesday saying he is on leave on Friday. I give him a task list that includes design doc, initiate code review and test plan. I saw the document and left it at that because no point reminding How bad it was after the person has said that he has given his best. The review did not start till late in afternoon and I dont yet know how much was complete.

He has not been able to adjust to team's timing,technical requirements nor has been able to help other teammates in their tasks for faster completion.

Even after all this mess the team is moving along towards meeting its goal but I will not be able to absorb tantrums by such resource on a regular basis.