One of the things I love about being a manager of managers is promoting team members into management. It's always a little bumpy, especially when they are taking over a team of former peers. Heavy coaching during this period is necessary and pays dividends. It's the difference between sparking a great future of management and missing out on a great opportunity.
One of the hardest shifts for folks in this position is making the shift from being an executor to being an agent of the company. When you are a manager of people, you now have the shift your mind set from "How am I going to hit my goals?" to "How is the company going to hit its goals?"
As I mentioned previously in the power of repetition, much of management is communication. On a daily level, that is usually around decisions being made that have impact on your team.
Once you become an agent of the company, you are no longer making decisions wholly on your own. Usually, there are other parties cross-functionally that have decisions that need to be made as well where you are an input, but not necessarily the prime decision maker.
In this case, regardless of who makes the final call, you will need to own the decision. You need to understand your team's needs, and you need to advocate for their needs as you provide input on a decision. You should frame these in costs and benefits and be instructive as to what your team needs to make the inevitable decision work.
Sometimes, what your team needs will be met and sometimes it wont. Regardless, you need to take that decision and own it. You need to be able to defend and provide context as to why the decision was made the way it was. At this point it is on you, and any frustration that the team feels needs to be directed at you, rather than to another team or leader in the organization.
It can be uncomfortable sometimes. This is where listening well and being empathetic as a manager really pays off. That's the benefit of the doubt you need to cultivate with your team that any other leader in the organization will have less of. Thus, all blowback needs to fall on you.
The skill you need to develop here is creative problem solving and negotiation. When you are in a decision making room and have your team's needs in mind, you need to diligently work on providing ideas and solutions that meet the business needs and your team's needs. You need to always hold both.
If you develop that skill, more often than not the decisions you bring back to your team will land well. And when they don't, you still need to take on the responsibility of the decision as if it is your own.
This will build trust between you and your new peers - the other managers in the organization, which will accrete making it better for your team and your standing with your team. A functional, collaborative layer of managers who trust each other makes an organization flow smoothly. Decisions are made quicker and better and ultimately the company (and the people you manage) has the best chance of succeeding