Situation is this. Husband and wife with 2 young sons attend Thai Consulate in Penang.

Wife applies for ED Visa with the necessary documents and it is granted.

The husband (and 2 children) applied for O Visa so that they may remain with the wife/mother.

Husband checked his passport and saw that he had been granted the O Visa but the children's passport were not checked.

Family arrive at Suvarnabhumi Airport where it was noted that there was not visa in the children's passport.

Airport Immigration granted permit to stay for wife - 90 days, for husband 90 days. As children had no visa, immigration granted them 30 day on arrival stay. This was all correct Immigration procedure. Parents have 90 days which will be extended every 90 days.

Now, what to do about the children stay?

Children under 14 will not be fined or deported for overstay, so it is not a total disaster.

Go to immigration and try to convert their visa exempt entry into a non-immigrant O visa. Immigration might do it, or not. Normaly they won't, as the person they are dependend on must be on an extension of stay.

As Lite Beer pointed out, no overstay fien for children under 14. You could also first look for a school, if they are of the right age, and with some letters from the school apply for a ED visa for the children next time they go abroad, or the O visa as your wife's dependends.