Hi L.:
I have worked in daycare off and on for many, many years and I will tell you right now that your daughter coming home dirty is not okay. I understand that it can be easier for some to make a mess while changing a baby, but then baby's clothes should be changed as well. I have never, EVER sent a child home with poo on their clothes. I have sent children home in loaner clothing if they didn't have a change for whatever reason, as feces on her clothes becomes a health issue for her and others in the daycare home. Please talk to your caregiver about how much this upsets you! I realize that with so many children in her care your provider is busy, but keeping the kids in her care safe and clean is not optional.
About the sleep; the last daycare I worked in was a 12-child group home daycare. At any given time we had 3-4 infants, as many toddlers and then a few older children. What we often found is that children who have very quiet environments at home did not sleep well at our daycare because of other babies crying and noises that could not be helped. Sometimes sleep schedules at home made if difficult for the children to sleep during naps. Eventually most in our care adapted, but if this may be the case with your daughter, then limiting evening naps for her at home may help a bit. Also, try making some noise while baby naps. Run the vacuum, play some music... if she wakes, let her settle herself back down without you (if you can; many moms find this terribly difficult -- I was among those!).
Infants under one year should be allowed to nap whenever they like and need to be offered the opportunity. For us, this meant keeping cribs set up in a separate room for those under a year old, drapes drawn, and music on to help drown out sudden noises from older, non-nappers in the next room.
The final piece of advice I would give to you is to visit your daughter in daycare at odd times during the day. This may be difficult for you or inconvenient, but it is worth it to take a peek at how your provider is operating. Do not alert your provider you are coming, just show up. It will do two things: 1. You will get a snapshot, good or bad, at how things are running at your daughter's daycare. 2. Your provider will never know when to expect you, and hopefully will be careful to provide care that you would approve of all day long to your daughter and others in her care.
Good luck to you!
J.