I find this extremely unreasonable.
When you choose to send your child to a childminder or nursery, you accept some risks...these range from catching a cold, to all manners of other health issues. It’s the reality of mixing with other people. If you can’t cope with this, you cannot really use childcare because no carer can guarantee what conditions they have or don’t have or that they will or won’t be passed on.
And you noticed her cold sore. If that was a real concern to you, it was up to you then to remove your child and not up to her or necessarily possible for her to prevent transmission, even if she was very careful.
I think the level of worry about the child have a cold sore is excessive and disproportionate. Are you a very anxious person Op. Is this really about you feeling responsible?
I don’t think anyone is ‘to blame’ for your child having a cold sore. Clearly with most conditions it has been transmitted in some way, but that’s life and if we have contact with others there’s a risk. If anyone needs to take responsibility (and I do t think they do) it is you, as you spotted the cold sore, which you clearly have a thing about, and continued to send him. If you had a serious concern you should have a) spoken to the childminder about it and your worries and asked her to be extra vigilant (still can’t guarantee it won’t be passed on) or b. Chosen not to send him. But you did neither.
Speaking to her about it now is really too late. The horse has bolted and it won’t achieve anything except bad feeling. If you want to leave anyway, give the necessary notice and move on, but get some perspective on this and the issue of blame.
It’s just one of those unfortunate things that happens frequently when children go to nursery or childminders, or to school...which they all do eventually.