I'm sorry your daughter is going through this - especially after being WR and seemingly getting back into life. And, of course, that you're having to go through this, too. I get the worry and frustration.
My guess from what you've said is it is anxiety related. It is a guess and others may have opinions but 1 year after IP and W/R, ahead of a stressful time, my d can still get nauseous. Sometimes she says: I don't feel anxious but she realises she can get the anxious feelings withough having anxious thoughts necessarily. I think she is more anxious when she feels nauseous because a) she doesn't want to be sick b) is concerned that we will think it may be an excuse or an ED thing so how it is perceived by you may also be a concern. So, then it becomes a bit of a cycle - geting nervous because of feeling nauseous and then feeling more anxious etc.
As long as she replaces the calories, you are covering your bases on the ED front is my feeling. And you have shown her this is not negotiable. I think you're doing great here.
My suggestion (and others may have theirs) is to fake confidence, reassure and keep calm, like it's no big deal.
This could be by saying something like:I guess this is worrying for you but I've read about it/asked an expert/Dr/dietician and it's really common - even when better if we feel a bit anxious for any reason. The advice is to get breakfast eaten with quickly and get on with the day. It will pass. Here, have a shake....
Maybe use distraction again - could you watch something together, talk about future holidays or something during breakfast
Are there 'easier' things to eat to make breakfast calorific but quicker? A smoothie or something? I know we don't want to get into negotiations about food too much but away from breakfast, what about suggesting: just for now while nausea is an issue, would you prefer this or this first thing?
My guess is she is as scared as you are, if not more so and so it could be that you could help contain this anxiety and keep it in perspective for her while setting parameters
Actually, just today I sent my d off with a packed lunch for college. She has the first of an important exam after lunch and so I told her: It's common to feel anxious before an exam and not feel very hungry but you realise you need to eat everything regardless, right? (Just heading this off at the pass......)
Well done on getting your d to this point. Hopefully this new breakfast thing is just an odd blip that can be overcome with calmness, consistency and a bit of time. Wishing you all the best. I'm sure others will be along with some ideas soon, too.xx