The tower fell on the wall, and walkers were wandering the town. I think she pretty plainly wanted to deal with this situation quickly so she could turn her attention on more pressing matters. The concussion didn't help.
A lot of people are pissed about Morgan. I understand this particular wolf is not likable, but at some point in a post apocalyptic world people have to stop killing each other, come to terms with what they've done, and work together to rebuild. You can see this theme in several of the characters story arcs, each one caring about someone who either wronged them, or they have no reason to care for. What emerges from that is a stronger group. This guy is particularly unlikable, and I don't think the audience tolerates Morgan keeping him alive. But again it's a spectrum across most of the storylines. Morgan is one side (all life is precious). Carol is the other side of the spectrum (look at the flowers), and they inevitably clash.