I am not very experienced when it comes to pointe shoes - I only got my first pair in September this year. My first pair were really bad fitted; I live in a rather small city, and when my school arranged for a lady to come and sell us shoes, she only had two different shoes with her. I ended up with shoes I couldn't use pads in, because they were too narrow (they were the best shoes for me of the ones she had brought, but they were still really bad for my feet).
I bought new shoes in a bigger city a few weeks ago, got properly fitted, and now I can even use pads! The point I'm trying to get to, is that the difference between pads/no pads is huge, at least it was to me. In my first pair I taped my toes and used a bit of tissue paper in the shoes, but it still hurt a lot. Now, with the pads, I don't feel any pain at all, compared to my first experiences with pointe shoes. I feel I am better capable of focusing on the dancing itself now, and it's also a lot more fun!
It sounds to me like your daughter is just not used to dancing without pads, and if you've gotten used to them, I can imagine it must feel really uncomfortable to suddely quit. As mentioned above here, I believe it would be a good idea to ask the teacher to explain better why your daughter should change shoes. It also depends on how serious your daughter's dancing is - unless she is going for a future as a professional ballerina, the most important thing is that she feels good when dancing and has shoes that work with her rather than against her.
If you decide to keep using the shoes the teacher suggests, be careful to breake the shoes in properly, and try using a lot of lamb's wool in the beginning to make it feel less painful. Tape the toes to give better support, and I would also suggest she just walk around in the house with them once in a while, just to get used to how they feel on her feet.
There are many out there who know more about this than me, but it is my personal opinion that the shoes should not destroy your daughters feet nor her love for dancing. Hope it works out okay!