There may be spoilers in this post, but only regarding that particular episode. Beware.
His decision was illogical.
I cannot recall names very well. I don't know what to call her.
The most pressing matter is the obvious interest Daryl has taken in the woman. He is the most valuable member of their team. He is strong and intelligent, yet nearly unquestioningly submits to Ricks command. In Daryl's eyes, Rick may have overstepped his authority.
That is a problem. Keeping Daryl in a state of submission is a primary objective in maintaining structure. It is critical that he remain dominated, and comfortable with his role as a subject. With this, the risk that he may begin to rebel is too high.
Without physical superiority, Rick has no way to maintain control of the group if this happens. If Daryl attacks and defeats him, his authority is lost. If you cannot beat someone you mean to control, be sure you never have to fight them.
The woman is a problem, however. Taking action on her own endangers the group and diminishes morale. It also threatens the establishment of power. She has created a chaotic situation, and destabilized a large, soft-minded man that could have been turned into a valuable fighter. She must be controlled.
There are better ways to accomplish this than Rick's decision, however.
If later it is determined that she must be eliminated, there are a number of ways to arrange it in such a manner as to increase the solidity of Rick's command. Any order involving her given by Daryl and mildly contested by Rick can be turned to quiet execution using the walkers. All it takes is a little time, and a seized opportunity.
Unaware, Daryl will assume again that Rick's power is warranted, and will further submit to his control.
If she is deemed too valuable to eliminate, there is a way to control her using her past as inspiration. It may seem incredibly cruel, but they exist in a cruel world.
Mind you, this is the opinion given by someone who would have been using the children to scout for supplies because of their drain on the effectiveness of operations, so things like this come to my mind.
All that needs to be done is to manipulate Daryl to anger, and then praise his action afterword. He is already one step away from being made into a dog. A further manipulation of his guilt as a result of the action would seal his fate.
The situation will resolve itself. In this, you have gained further control of Daryl, and tamed the woman; whatever the hell her name is.
During the mission in which Rick made the decision in question, and as a result of his inaction and action, he also lost one extra vehicle, two firearms, and a number of supplies, including a valuable roof-top cargo carrier. The carrier alone is a great loss, for a number of reasons involving both daily function and practical combat operations.
Cheers,
Kennith