Remember she's the survivor of abuse. She's probably developed a "hard core" that she retreated into during the abuse and now it serves her just as it does Carol, to be able to do what's necessary.
For Carol that development took a very long time though, and isn't necessarily the logical outcome of being a victim of abuse. Something about that whole scene just rubbed me the wrong way. Maybe it was because she then took time to make like the 3rd speech of the episode. It didn't really seem natural.
Sometimes shows like these that have such rampant death don't really treat their characters like real people because most would be very apprehensive or nervous about it. FTWD had it way worse.
I hate to sound like I'm ragging on this episode though. I thought there were several good character interactions, like Tara/Denise, Aaron/Maggie, and Spencer actually became an interesting character.
Remember back to the black and white flashback scenes in the season premiere. They seemed to indicate that there was a decent gap between seasons. At least a few weeks. Still would be considered a short timeframe to deal with a death like that (or for Deanna and her son to deal with Reg's death), but in the TWD world, at least they had some time.
Yeah, it might have seemed like that, but other things don't quite line up. I think they wouldn't have wanted to skip that much time because it's hard to believe that certain characters, like Morgan, would isolate and not resolve any issues. The pace ever since they reached Alexandria has been too insane to have a period like that without much happening.
I know it's not official, but there's the Walking Dead wiki timeline, which assumes about five days. Scott Gimple isn't very fond of this kind of tracking though. On one episode of Talking Dead he kind of avoided any questions about dates and times because it's just the way they tell stories (I think this was as it related to Judith's age). There's all sorts of time problems on this show, probably the most notable being how long Rick was in a coma. There are others like people healing rather fast or Carl's aging. Some of that has more to do with the fact that 1 season doesn't exactly equal 1 year. They have to feel out when things become too sudden (Rick/Jessie hookup) or when they're being too dragged out (Sophia, Glenn, Beth, etc).
I don't think we'll see anything with Glenn until midseason finale.