If you can arrange the correct papers to have her permission to travel outside of Thailand all lined up ready for her to sign, I would think of a reason for your travel, holiday to Vietnam for a week or parents haved died, a story to tell her, play as if you are only going for a short time, not as if for good. Do not argue, maybe as someone said offer some money to have it signed. It is a game of chess.
You mentioned you were married to her but divorced but are legalized as the father, check on the paperwork so there are no surprises for you. The other thing is you could try a land border crossing and see what happens, act as if you did not know you need papers to be signed. If you get turned back not a huge money loss.
Good luck