Let’s cut through the bullshit. The only way if your mum is not documented as you say is she needs to be in Thailand and will need a family member to vouch for her plus be registered on the house address. A birth certificate helps. Once those things are establish birth certificate , house registration and family members to be present with her at the Amphoe. You will fill in a shit ton of paper work and if she has Australian citizenship that must also be translated into Thai as also her marriage certificate. This is just to establish you for a Thai ID card they will notify you when to go back it can take a few months it depends. Once you have your Thai ID you can then a month later apply for your Thai passport.(has nothing to do with immigration)
I went through this in 2013 to have my Thai citizenship reinstated having lived in Australia as an Australian citizen for 40 years. Now I have dual citizenship.
Oops .. as long as your mothers name is registered on your birth certificate and she can prove who she is in Thailand with family members to help her.
You will need your Australian citizenship & birth certificate translated and be present at the Amphoe where this is all done . They are the ones who determine if they will issue you a Thai ID based on the documents you are requested to submit. It takes patients believe me and if you want it fast an envelope helps 😉
She certainly can get Thai citizenship ID. Though she will need the house book of the address on her Thai birth certificate. The process can be long or short depending and a ton of paper work (everything must be translated to Thai from German )and signing. It’s a pain to do as an adult. They will issue you the Thai ID takes 1 month (my case) and you can then apply for your Thai Passport, which is the easiest step of the entire thing.
I’m Thai & Australian . I hold both passports and live in Thailand permanently and just went back to Aus for Christmas . I had to book my return ticket in my Australian passport and on leaving at the airport I just went through the Thai queue at immigration and gave them both passports as I live here as a Thai and was stamped out on my Thai passport . On entry to Aus I just scanned my Aus passport and on return to Thailand at Thai immigration I scan my Thai passport. They link them up so it’s a no brainer.