Snippets - firstly I feel it is rather misleading of you to call your nanny a Childminder. You have subsequently corrected that but I don't feel you should have used the wrong terminology to start with. There are many good nannies and childminders who post on Mumsnet and we don't want parents to get confused about the different types of childcare.
As a parent who employs a nanny, you have a lot of control over what that person does, whereas with a childminder, parents are using a service and thus have no control over how that service is run.
If your nanny is not following your instructions, then correct them (making it a written warning if you feel it warrants that level of disciplinary action). Employing staff is never easy, disciplining staff is hard but moaning on here won't get you very far I feel... you need to have a chat with your employee and sort out your expectations v what is happening day-to-day.
To answer your original question... Yes you are unreasonable (as a Childminder is a service provider, not an employee).
To answer your Revised Question... No you are not unreasonable - a nanny is expected to comply with your wishes as much as possible, given the circumstances at the time. Thus I do not feel it is unreasonable to expect your nanny to have cooked food from scratch, if that is what your prior agreement was.
As a nanny the vast majority of the food the children I care for eat, is cooked from scratch. However not all food is cooked from scratch... my employer does buy processed baby food (handy for when a toddler wants food NOW... not wanting to wait 20 minutes), also can be handy on outings, and also when a child is feeling unwell (toddlers seem to like going back to mushy food when they are feeling off-colour).
We also have food treats - a packet of crisps for example is a treat whilst out on an outing, or as part of a picnic.
Anyway starting to get away from the point perhaps. I feel that it is perfectly reasonable for you to be annoyed with your nanny (an employee) who has fed your child something which you have told them that they should not have. If however you have not told your nanny that such food is not acceptable, then while you can still be annoyed about it... you can't blame your employee for doing something that they were not aware was not permitted.