If her Thai ID it’s show her live in Sa keaw province, she can use ID for cross border (ask for certificate at government officials hub in Sa keaw) but if she not live in another province that she must need passport.
I really understand what you want to do. I heard someone they driven car from Europe to Thailand but it longtime. And I found Thai man driven from Thailand to Italy.
it’s quite dangerous in my opinion. You can visit but not guarantee it’s 100 % safe. In Pattanee province has Ko Losin you can diving for see Sharks and mantas. Narativas it’s good for trekking in the wild, it’s name Halabala mountain. And Yala the most famous is Betong it’s mostly safe in this 3 provinces. All of this you should go by private car and it’s better not stay some place for long time.
Why and where are you interested in this 3 Southern provinces ? Because it’s not famous for tourists. But if you want to visit Ko Losin in Pattanee province for diving it’s good.