It does take a lot of getting used to, and you do have to trust your instinct. However you have to also trust the CM to a certain extent otherwise you will never have any peace of mind. I remember pig's nightmare and my own a couple of years ago (went sour after a few excellent months) , but you have to sort out and get a bit of perspective on what is acceptable and what isn't and talk about it.
The puppy. Did DP ask about it? What did they say? What kind of dog is it? What safeguards are in place to give both pup and child me-time (I think there are rules about it).
Can you reasonably expect your CM's DH to never be at the home? And why would it matter? It is his family home.
And for the sleep thing. Again, it's annoying, and needs to be discussed, but she may have considered, using professional experience and judgement, that T needed an extra half hour or whatever it was.
I get that there is a cultural difference in the way that you guys and I see childcare. Over here mindees fit in with the family life of the CM. And if I shouted at nursery about leaving lo to sleep a bit longer then they'd laugh at me (they would be open to discussion of course).
The key points though are, are you satisfied T is being looked after, played with, stimulated, is happy, safe, eating well, and sleeping well? The rest is just detail, to be honest. You can't completely control how others manage your children.