that is the same as the information I was given when we shipped 8 years ago. I was on a Non 'O' but avoided import duty as my wife was a Thai National. Can't say if things have changed and Brian Ash is correct.
the children being on a house book is very important in Thailand. Without that they will not be able to go to a Thai School, get ID card and many other Thai benefits.
if the father is on the birth certificate you can go to the Thai Embassy in Sweden to obtain Thai Birth Certificates. Then you can get Thai Passports for them. If you do not have time to do that, enter them on visa exempt. Stay on overstay until you get the Thai citizenship sorted. There is no penalty for overstay by minors.
You need to do the citizenship so you can put their names on a house book registration