Have they admitted the kid was or was not wearing a mask on the way there? I have not seen that.

But if the kid was not wearing a mask on the way there then yes that crew needs to be disciplined. I don't know what Southwest's rules are for firing employees so not clear if this incident would rise to that level. However airlines have made it very clear to customers if you do not follow their mask rule they will "fire you as a customer." Their failure to enforce policy the first time put all of the passengers and crew on their first flight at risk not to mention empowered this mother to think she was above the rules - assuming the kid had no mask on that inbound flight which we do not know.

Maybe the kid accepted the mask on the way there for some reason...