GG I wouldn't be happy with it either for all the reasons you and others have said (being her tv rather than kid-specific, relationship between childminder and child v different to that of child and parent etc.) BUT I wouldn't dismiss her right away if you have otherwise been happy with her care of DS2.
If you remember, I had an issue with DS's nursery a while back where they left him in dirty nappies two days running. I was furious and my initial reaction was to pull him out of there and find something else, but on reflection I decided to have a calm chat with the manager about it and actually I'm very glad I did. Nothing of the sort has ever happened since and my DS is happy and settled. Overall their care of him and the other LOs is excellent (as poppy said, I like knowing he gets three exciting activity-packed days guaranteed every week, in case I feel like being a little more slack ). Yesterday when I dropped him off, he ran into his keyworker's arms with a great big grin
When you took her on, did you have a thorough talk about expectations and rules? I only ask as it seemed to be a fairly laidback appointment process, and in those sort of situations it's easy to overlook the more difficult stuff for the sake of a nice atmosphere (I know, because I do it myself all the time). Before you get rid, it might be worth sitting her down and having a pleasant-but-firm chat about what exactly you expect her to do and not do. Draw up a contract, even - it will help both of you know where you stand.
Then, if stuff continues to happen that you're not jazzed about, you'll be able to reassess from a clear starting point.