You may have heard of this happening but 100% this is hogwash. You don’t ask for however long you want to stay for. If you are granted entry to Thailand you are given the number of days your entry scheme allows. That may be 14, 15, 30, 60, 90, 365 days, or longer. You don’t decide what to ask for. Your entry scheme, as in the visa you may or may not hold decides.
Any foreigner would need a visa that permits work and an accompanying work permit to work legally here.
But your post suggests that the child is Thai - with a Thai father so for all intents and purposes they are Thai and therefore they could work. The fact that they also have a US passport is irrelevant