You don't say if this is a half-day or full-day program. For me, this would be good information.
And "paranoia" aside, as a preschool teacher and care provider, these are the things that stand out to me:
A rest time/quiet time should be a scheduled part of a child's day. All the children need this downtime.
I'm getting the feeling that TV is used as a babysitter. If children are falling asleep in front of the television, this isn't good. There should be designated spaces for children to rest their bodies comfortably.
If it were me, personally, I'd be looking for a higher quality of care. There are plenty of in-home daycares who pass state certification, have some curriculum and age-appropriate daily schedule. They might also appreciate the environment of a larger certified child development center, where there are co-teachers in each room and director oversight. This would create a community of eyes to watch over their child.
Lastly, this whole situation has ruined the trust for your sister and brother in law in regard to this provider. The death of a child is terrible by any circumstances, and for him to have lost his infant daughter at a provider's home is just awful. My questions would be-- has he been able to trust other care providers; has he had grief counseling/counseling around this? If they are able to find someone they *do* trust in the near future, this will be an assurance that he's getting more comfortable with trusting others, however, if this upset and suspicion (and I'm not saying whether it's warranted or not, because I do not know the 'truth' of the situation) continue with other providers, it would be helpful for him to find resources to help him heal.
What a hard situation. Your family has my sympathies.
H.
Added: I know that in our state, I have to have pre-signed forms for administration of medication. This means tylenol, motrin, (I even have a signed consent for sunblock), any antibiotics. I'm very by-the-book on this and always get adult verbal consent before giving any medication, and keep a log too.