I had only recently turned 12 when I first got my period. But to be honest, I wasn't embarrassed, more excited. I had to wear our neighbour's pads for the first day, then my mum bought Mini Tampons. She had the "this is all normal talk" with me, then she let me choose whether I wanted help with the tampons or whether I wanted to try for myself. i just followed the instructions (it had little diagrams) and didn't end up needing help. I never looked back and the next time I had to wear pads was after giving birth to DD ;-)
Now, that story won't help you. But I just find it hard to believe that your DSD is so embarrassed or in denial that she won't wear pads or tampons. Is she usually a very shy girl? I would definitely try and reason with her (hygiene, piossible leakage, extra work, etc.). She's old enough to understand. Had she been told about puberty and periods before getting her first?
If she claims she doesn't want to wear the because she doesn't like them, then I would ask her to specify: "What don't you like about them? How could they be improved?" to try and get to the root of the problem. Wouldn't walking around with bloody undies be very uncomfortable, too?
I found pads extremely uncomfortable, too. So maybe she might need some help with the tampons? I don't know how close you are with your DSD, maybe this is something her mother should help her with???

I hope you can sort this out.
Sasa