No, it's hearsay. That is it would be being adduced not only to prove that that the witness heard it or that the mother said it, but to prove that what the statement contained was true. Now, if I come in and say to someone "It is raining" that is not admissible to show that it is raining, and it does not become proof because they hear me say it and recount the fact. If they ran and got an umbrella, they could speak to that fact alone, and might be allowed to say that they did so as a result of what they heard, but the statement itself is not proof.
There are exceptions, clearly defined: saying how old you are, for example, and admissions by an accused, and things said in the agony of the moment (res gestae: lawyers love Latin) when the witness didn't have time to think or lie, but they are limited.