Nettie ending up dead is the result of the player making multiple poor choices, not dice rolls.
Unless of course you want to kill Nettie . . which is a valid choice.
Nettie really needs to die. Someone who poisons people without their consent when they ask for her help really needs a quick execution.
On the OP's point though, I somewhat agree, but not entirely. What we need is:
1. Better estimation of difficulty for the DCs. If it is a trivial(ish) task make the baseline very easy, e.g. a strength check of 5 so that anyone with a decent strength modifier is very unlikely to fail. (I think it is good to keep them though, because a strong character can fail a strength check on a 1, modelling them fumbling it.)
2. Keep it to one skill check per situation. I agree it is annoying to pass one skill check just to give us another.
