When to use "他的太太" and when "他太太"?
When you want to express possessive relations concerning family members or relatives, you don't need 的. 

我妈妈，你爸爸，她男朋友，我们家老大, etc.

I have done some searches with different expressions with and without 的, and I see that this rule is not applied consistently. 

EDIT: There are ambiguous cases, e.g. 你们孩子 could mean "You children" or "Your children" (with plural you in both cases, of course). In such cases 你们的孩子 would make it clear what the speaker means.