I can only say what is normal for Oklahoma. An infant is higher because they can only have 4 baby's per staff, 6 for toddlers, 8 for 2 year olds, then 12 for 3 year olds, and 15 for the 4 year old class and up to 20 per staff for school age kids.
So yes, it is normal in facility child care for the price to go down quite a bit as the child gets older. My computer crashed and I don't have the web site on this laptop. Almost all of my other child care questions about rates have the link in them. Maybe you can use the search option on top to find other questions on this topic.
For instance, a newborn in a 3 STAR facility, which is the highest rating a facility can achieve in Oklahoma, might get paid for a state paid child $30 per day, that is normally a 10-11 hour day too.
Then a school aged child in the same facility would only pay $15 per day. That would be year round too. In school all day and out for summer. That way the provider gets a full amount even on a part time day after school.
I think that if you call around you will find out if her prices are comparable or not. She was hurt you felt her care wasn't good enough for your older child. She took it personally. If she is advertising that she is offering those advantages you were looking for but they weren't good enough for you then she probably felt she wasn't as good as she thought she was or something along those lines.
I would move both kids to full time child care in a full facility. They often have more resources and if staff is sick or needs time off they have other staff in the facility, such as an assistant director, who the kids know and love to fill in.