Hi Sophia, I am sorry if I am misunderstanding but your daughter has only been in daycare for one week and had 2 fevers, didn't nap for the week and was different that weekend and during the night? Has anything gotten better since you posted? I notice it has been a week and there haven't been updates or replies.
My question would be about the transition that you did to the daycare. When we placed my daughter into daycare, we did it over a few days and so did all of my friends as that seems to be the norm. We took her the first day for a couple of hours and stayed with her, the second day for half a day but I stayed for the first 2 hours, the 3rd day I didn't stay long but she only stayed half a day, the 4th day, I dropped her off and left immediately and she stayed 6 hours and day 5, she stayed 8 hours by herself. We found that making the transition over a period of time, made it much easier on everyone. However, regardless, it is a change and never will be perfect.
Are there many other children in the daycare? Does your daughter get to take a special blanket with her or something of yours? What is your drop off and pick up routine like? Did you do many activities like Early Years Centers, circle times, playdates and such before or is this a very sudden change for her being around other people and away from home?
Also, some children are just much more structured and find change difficult, just like adults. Some are more go with the flow then others. Your daughter seems to be experiencing separation anxiety and some fear, in my non professional opinion. If she has been with a babysitter, family members, friends and in lots of social situations before, then this may pass quicker as she adjusts. If she has been mainly with you and dad and not left with anyone before or rarely left, this is probably a huge shock to her and difficult for her to understand.
My suggestion is that if you feel safe with the provider, to keep putting her to bed really early. At her age, 12 hours a night is not uncommon to be honest. Sleep also begets sleep and you may think that sleeping longer at night will keep her from napping but that is false. Read "Healthy Sleep Habits, Healthy Kids" for more info. It's an interesting read and goes from newborns all the way up.
Your daughter may also be sensing your stress and feelings of guilt or frustration. You did say that it was wearing on the whole family. Children are super sensitive and she may fee the tension from you. Therefore, I highly suggest taking care of yourself and getting as much rest as you can. If your child needs extra love and coddling right now, give it to her. It's not a big deal, she is only 1 after all, not a teenager with survival skills. When you drop her off, make it quick as prolonging it makes it work and they will play on that. Children are very smart and once they know a behavior is working to get them attention, even bad attention, they will keep doing it.
As for naps, our daycare provider asked us to bring a blanket from home and some kids had special sleep buddies at that age too. It's really hard to sleep in a strange spot so maybe ask your provider what the routine is and work together to make the bed and routine as similar to home as possible. If that fails, have the daycare provider wear your daughter on her back or front as she walks around or does stuff. Guaranteed pass out. Just make sure it's a really good carrier like a Pikkolo, Beco, Tula or Ergo. NO BABY BJORNS! They don't align your child or the person carrying the child properly and cause undue strain, pain and can be dangerous. I find that even now, my almost 3 year old will pass out if I wear her or hold her close.Women around the world wear their children all day long for a reason.
If things to improve and your daughter is still getting sick all the time, not sleeping and things are just awful, I would speak to my doctor. You could also try a nanny share so your daughter is at home in her own environment.
I wish you luck and hope that things have improved for all your sakes. One week is a very short period of time to expect a baby to adjust so I may have misunderstood your post and apologize if that is the case.