This question is really interesting to me. You are not saying anything about the father (if there is one) and that factor could influence too how the boy speaks.
I don't know Mexican culture well enough to be sure what the boy would say if both parents were Mexican, but it is interesting to me how people in the States say "My dad/mom ...". Never "My father/mother ...". They seem to distinguish between someone who is a father and someone who is a dad.
In Spanish (at least Spain) you would address them directly as "papá/mamá" but talk about them as "Mi padre/madre ...". Only kids would use the "Mi papá/mamá..." form to talk about them.
My bet is that the mother would teach this kid to call her "mamá". In his environment outside his home this kid would be hearing other kids using "my dad / my mom", which he would associate with "papá and mamá". For all these reasons I am pretty sure that this boy would use the form "mamá" to address directly to his mother when talking to her (and he would probably use "mi mamá" to refer to her to other people).