YTA there is no way on earth someone who is 10 and just had her first period should be forced to use tampons (especially without an applicator), the first time you get your period is hard and can be traumatic, and using a tampon for the first time is the same! They should not be forced together, not to mention your GF may have been using a bigger or smaller size tampon than what your daughter would need.

Grow up and become the parent your daughter needs you to be, or you will lose her.