No worries. I didn’t know there was a reply limit. Might be because you are a new poster.
I think people here are going to be limited in what they can do. If it were me, I’d look for a way to make it easy for your daughter to find you when she is old enough to contact you if she wishes to (so, a search for your name and her name would turn up a way to contact you).
Otherwise, I imagine your best bet is working with Taiwanese courts and/or visiting in person. People here may have advice on courts or visitation, and I know I’ve seen posts in the pasts about parents who were cut off, so you could reach out to those posters and ask them for advice about what they did/how it went.
If I got your story correctly, it seems the only way you have to contact them is through a phone number. And that when you call this number, they hang up because you only speak English.
If so, try to find someone near you who can speak Mandarin to help you get through the Gramma and reach the Mom.
Or maybe they blocked you because they see you are calling from an international number. If so, try to use Skype to call them, and it shouldn’t be blocked.
Or try both at same time (Mandarin speaker + Skype call)
Best luck to you!
You can hire a private investigator. Google search for detective or private investigator Taiwan, and you’ll find at least 10. Check their websites and call to find out which ones have English speaking capability.