I believe that the children are aged 2, 2 and 9.
The first clue gives a variety of answers (any combination of the divisors of 36 = 2x2x3x3)
The second clue would then give the insurance salesman the opportunity to narrow these down substantially. Although, not knowing the number doesn't give us any insight. BUT the fact that the salesman is still unsure means that at this point, he must still have more than one possibility. After working through a few combinations of the divisors, I realised that if the next door neighbours house number was 13, then this would give the insurance salesman two choices, [2,2,9] and [1,6,6] and thus he would be unable to answer.
The final clue isn't the fact that the child is learning piano, but the fact that she has an eldest child implies that her eldest child is not a twin and thus eliminates the [1,6,6] possibility leaving only [2,2,9] as a possible result. (I'm aware that the woman may have two children aged 6 that are not twins, but ignoring this is the only way I can gleam any insight)