C.S.
Maybe let her do it herself?
My husband was the one that taught the teeth brushing. He took our son to pick out the brush he liked and toothpaste then every night and a.m. he brushed his teeth he would get a quarter. For the first week daddy went in then after that our son was required to do it himself. Yes at three. Footstool and all. Of course, I check and make sure there isn't a mess or if help is needed but I usually watch and chat or brush my teeth too. No need for me to get physically involved.
You are creating a habit. Once done, it sets in and they know what to do and you just have to make sure they go in there and brush before privileges - like story time at bed.
We no longer reward with money.
Also - kid's teeth are so healthy at that age - no vigorous brushing needed. Try raw carrots and rarely any candy and you will be okay. Our dentist said as long as the paste gets in their mouth, that is enough to fight bacteria.
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She's just showing a little independence that is all. It's a good thing - you want her to learn to do this on her own and want to do it for herself.
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I also find teeth brushing a happy time. Something about the water running and looking at themselves in the mirror. They are so funny! Enjoy this time as much as you can!
To happy teeth, C.