Having the name on the birth certificate is absolutely not enough! You MUST have the custody of your daugjter written on the official paper, then you can get a visa easy peasy :)
I remember applying for multiple entry tourist visa years ago! In Cambodia and Lao :) After 15 years here, I've experienced ALL visa types! I am currently in Thailand, I just need the requirements; 2 photos, 20k in bank, METV application form, a picture of my cousin's dog? etc. :D
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