I tried bribing her with 100 gold and she took 3000 and said "This is more like it" and laughed. So I did it again, 'cause I felt like it.
Anyway, took her out and we were attacked all at once by 3 big bads. She died before I killed them. Used to playing Skyrim, where my followers are told not to die. So I saved up and got her a full set of glass armour and a daedric short sword. Will take her out again in a while and maybe tell her to hang back a bit when in combat.
No issues with Constance. She's great, Just like Vilja.
Many thanks.