This is a particularly difficult situation and like you mentioned it can be quite awkward. I haven't really been in this situation but what I have learned from others is that they are able to deal with this situation by the style of leadership the often adopt.
You must master the more participative and democratic style of leadership in this situation and at this level. A participative style of leadership does not mean you surrender the decision making to others, no, you only lead them to make the best decision, which most likely is what you already have in mind. This will bring a feeling that you are carrying them along and everyone is part of the decision making, even the difficult ones. Remember, they assume/feel they know as much as you do and are qualified to lead as much as you (which may even be true). As time goes on, they will begin to trust your judgement and leadership.
Note that this style may not work in all cases because of the main drawback of delaying decision making, but never attempt to be bossy. When you make a decision always give an explanation. Seek for their immediate feedback but still hold to your decision.
I hope this helps.