Another option that you have
@Jannik *****
is
Rather than bounce out and back to get a 30 day free entry and then apply for the Non-O inside the country why not just go to the thai consulate in Vientiane or Savannakhet Lao and apply for a 90 day Non-O visa based on being the parent of a thai child.
You can get that for 2000baht with just your name on the birth certificate, and copies of the thai mother's i/d & house book listing..
That way you when you come back you'll get a 90 day entry stamp and can go for the year extension from that once you get the parental rights decree sorted out
That would cut a few steps out of the process and as you said you have to exit/re-enter anyway (y)
Just a thought