I think your response to him when he thought he had a minute could have been something more like "a sub must report to the table within 30 seconds or it's a technical foul by rule." Of course that is easy for me to say after the fact
I also don't think you can/should wipe the slate clean. I think you should do whatever you did right to make the coach upset in the first place but be the same for both teams. It might work out that you have to make some tough calls against the other team and the coach will see you don't care about any personal issues. It might turn out that you have to make the same calls against his team and he might think it is personal. Your consistency will eventually let the coach know you are going to be the same every time out. I would also mention that if he does something to deserve a T don't hesitate. Same for the other coach. Finally, don't back down from this coach in any way. Look him squarely in the eyes when shaking hands and answering questions, if you can. If he sees this from you my signature line will apply and he will hopefully focus on coaching his team.
As others have stated your pregame with your partner is vital. I'm still of the mindset that you should build confidence in your partner(s) beginning with the pregame. You don't want him on the defense before you leave the locker room. Promote the crew concept over and over again. A harmonious crew is a thing of beauty! Have fun.