I'm a high D trying to improve my relationship with a "people focused" peer. We have had conflict over a project. I want to improve my relationship with this person, but he seems to want me to refrain from all input about his group's activities. My boss (high S?) and I both think that it would be problematic as my group and my peer's are very interdependent. My boss happens to agree with me on the facts of this particular issue but has told me that I must improve my relationship with this peer. We have a peer 1-on-1 coming up soon. Both of these people are people that I've worked with for a long time and think I know quite well. Any advice?
At the same time, I am trying to help a high D direct (individual contributor) improve his communication. He has been rubbing others the wrong way with his input on projects. I usually agree with him on the facts, but am trying to help him see that his bluntness is sometimes ineffective.
I just listened to "High D Manager Simple Downfall" and it reflects much of what I and my boss and my direct have been discussing about the mistakes that high D's sometimes make.

Invest in relationships - treat as a project?
Not sure if this is correct, but as a fellow High D I have looked at relationship-building as a project in itself. This takes my High D strength put puts my focus on results towards relationships. The flaw may be that it might come across as inauthentic. I'm not sure. But, that is what I am doing right now. I focus in 03s on the first 10 minutes over all else for now and push myself to learn one new thing about folks around me. So, in your case, I might focus on relationship (as a project) over the actual project results.
On your second item, I have been providing feedback on how my directs speak to other people. So, I recommend the feedback model: When you tell people you are frustrated with them, they feel judged and I have to come to your defense...how can you do that differently in the future?
I agree but...
Sounds like your boss says they agree but... it doesn't seem to be clear WHAT they agree with. You'll need to decide if they agree to "just the facts" and are saying in fact you're correct AND this relationship is more important. It's likely you & the other person will both carry a "they don't get along" name badge unless you resolve it yourself.
I'm still trying to figure out a more reliable approach to this. My opinion is that if you produce and you're not a jerk then let it go. So in situations like this I have to remind myself of the statement effectiveness comes before any other ethos. This means that if your effectiveness is at risk because of a poor relationship then it IS important.The worst case would be if you're both producers and you're both not really "jerks" per se. At that point be the person that can manage around the person almost or avoid them.
I learned something a while ago. You can't care more than the other person (you can but it's not effective) or your manager and you can't MAKE someone do anything including work with you. Be sure that you can show how you're being a team player. You need to be able to answer these interview behavioral questions:
1. Did you ever have a time when you didn't get along with a colleauge?
- What was the situation?
- What did you do?
- How did it turn out?
If you can answer these confidently then you've prepared for the other person raising an issue instead of being the person that seems like you're right in the middle of the complaints. Hope this helps, cheers