OK, so do you take her to your nanny job when she is supposedly sick? How can your DH justify that??? If nothing else, tell him the other parents don't want to risk their child becoming ill!
For starters - you need a zero tolerance approach to her "illness". I learned this from my mother and practice it with my SCs.
In your case, you cannot possibly take her to the home of another child when she's ill (yes, we know she isn't really - but this entire strategy relies on you completely sympathising and committing to the idea that she is really, genuinely ILL!). So start there. Next time she's sick, you either can't look after her as you can't expose the other child, OR you have to lose the day's work.
Next, she needs rest, of course. Lots of uninterrupted, telly-free, unstiulating REST. Talking on the phone will just keep her from her rest, so probably best to remove it for her own good. Reading a nice book is fine, unless she's complaining of headaches, in which case a semi-darkened room is quite nice.
Food. She should have soup and toast, perhaps, unless it is a severe stomach illness, in which case perhaps some dry crackers.
Obviously you don't want a relapse the following week, so it is advisable to talk to her mum and make sure that all weekend social plans or taxing activities are cancelled. (As her mum is onto her as well, this shouldn't be too hard.)
You say you tried this last week - good - keep it up and never backslide. Going to school has to be the more attractive option.
If there is something at school she does not want to face on Thursdays, she might actually fess up and tell you that. But if not - well, you can't help that and you can't indulge this behaviour.
Don't put up with threats from your DH over this, either!!! If he doesn't like you takingher in to school late - tough! He's not there, is he??? I would think it were absolutely worth the row. He's the one taking the piss, and you are ending up with all the hassle - plus setting up very bad behaviours as DSD becomes a teenager (trust me on this, please!).
(I also have a DH who lets DSD play sick and it is very annoying - but nothing like the degree you have described here! And I'm not left as the caregiver when she's malingering!)