I may be reading too deeply between the lines here, but here goes:
A nursery worker may have a tendency to give you feedback on concrete events - eg, he ate x, he had y dirty nappies. This is because this is firm evidence of care. It is hard to say "He's been happy today" if you have been conditioned to respond with hard data. This is true of many childcare workers, ime. The trick is to present the facts within an overall account of the day, ie including your child's feelings.
To extend this, the focus is then on eating the correct amount, not having accidents etc., and the importance of wider concepts - like having fun, working towards encouraging good eating - diminishes.
I think your nanny may be thinking that to do a good job she has to present you with well fed, clean cildren at the end of the day - all the perceived 'good nanny' boxes ticked.
It's my experience as a nanny/childminder/au pair/creche worker/night nanny that what parents want is a happy child. To achieve this, you need to observe,listen to and understand the experts on the children in question: the parents. I think a good nanny will tell you "He didn't eat much lunch I'm afraid, but he didn't get upset, and we had a lovely time in the sandpit" over "He ate a good lunch but I had to nag him into it." Which would you rather hear?
So to summarise, if you feel it's worth it, I think you should - as you have been - continue to 'parent in capitals' (great phrase!) and clearly instruct her on exactly what is important to you, only you know her and will be able to see if and how she responds to that.
If she can't conceive of losing the idea that badgering children into doing something (eg eating) isn't what you want, or will work for your children, well, yup, she needs to go.
She clearly has little experience in being a live in nanny (frankly, she's not the sort of houseguest you'd invite back, is she?!) and doesn't sound as if she's being very kind to the children. I would never and have never treated children in that way. Agree wholeheartedly with ST about her dragging childcarers into disrepute!
However, over the weekend, I very much hope she will surprise you.
If she doesn't, try gumtree.