Since she is pictured on the cover and the credits page, I'm pretty sure the mom is still alive. I don't think any of the other kids will survive though.
Its rather clear the vorpal bunny finished off her siblings for exp. Telling them to fight but avoid fatal wounds at all cost, not stay alive, not survive, but that it was ok to take wounds, just not fatal ones. Wonder if she killed the slime as well.
As for the mother I actually like her odds. She was slashed in the lower abdomen. Gut wounds like it while very fatal also are known for being extremely slow deaths. WW2 soldiers who were gut shot were left for dead as there was no hope for them, but they would slowly die over the next several hours. But this is were its good for her, the reason its so lethal is that the intestines tend to contaminate the wound making it a very tricky wound to close or treat as you have to close it both internally and externally. But if we are talking magic its kind of the reverse. Potions and magic tend to have little to no trouble with small delicate work and quickly sealing bleeding without the need of physically reaching the area. So this sort of wound gives them a lot of time and if they have potion or magic they are able to bypass the biggest problems with the wound.