M.R.
Just a couple questions to begin with - Has she always skipped a morning nap then taken an afternoon nap and a late afternoon catnap? Who is this schedule for - your best interests or your child's best interests?
Don't get me wrong, I'm all about having my child on a routine or a schedule. I think it is very important that children know what to expect out of their day AND receive adequate sleep that is needed. A lot of research will indicate that an 8 month old will typically still be taking a shorter morning nap and a longer afternoon nap. Additionally, most children that age should be receiving a nap after 2-3 hours of wakefulness in the morning. I think it is disrespectful to her sleeping needs to force her to stay awake. If she's falling asleep on the floor then she is obviously tired and needs a nap. Furthermore, forcing her to stay awake could be the root of the night-waking problem due to being overtired. You may wish to read "Healthy Sleep Habits, Happy Child" by Dr. Marc Weissbluth as it is based on over 30 years of infant/child sleep research. It may even be able to assist you with the night issues you've been having.
If you're that dissatisfied with this childcare option then you may feel more comfortable changing to another place. Despite an age difference, I like to keep an open mind when my childcare staff members discuss childcare with me since they've likely dealt with many, many children.