Been with AXA for years. Never had problems with them, always had my claims paid within 6 weeks. OPD under 50k is paid directly by AXA for my insurance.
That's what I told them too. Why in the world would the mother give up those rights. I had a visa for Thai family one year extension based on son in Khon Kaen prior coming too Phuket. In Phuket they wouldn't have it and told me this. I ended getting a yearly marriage extension and drew an especially nice map for them.
It's an international permit that is only valid with your original lisence. Basically it's a translation from your license into English. If your license is already in English you shouldn't have to get a IDP. However, this is Thailand and it might be worth to get it just in case.