It's been a stipulation for a long time however never enforced. It seems now that they're clamping down on everything and looking for excuses not to let people in.....this being one perfect excuse.
I was under the impression that you also had to be the legalised guardian of child as having your name on a child birth certificate in Thailand does not actually give you any rights or responsibilities to that child. I spent a fortune going through all this earlier last year
If you can't meet those credentials then I'd get tourist visas until you can. I've been in the same boat as you. I've also had the same warning at Suvarnabhumi, however and then entered again on visa exempt with no issues a few weeks later....