Don't use gloves. Clean bare hands makes things a lot easier.
Calcium Citrate many say has helped the hen push the egg out. Also a warm bath with Epsom Salts has been successful.
Diarrhea is a common problem with hens and is very difficult to treat. Moulting hens seem to be prone to it, possibly because some, especially ranging hens, eat a lot less commercial feed and tend to forage more. Usually it sorts itself out over time. I suggest you weigh the hen your concerned...