The relationship of 我 and 咱们
The meaning of 咱 is different in northern China and the rest.


In east-north China, 咱 is the same as 我. People there say 咱 to refer
to him/herself. And it depends whether the speaker is endearing
him/herself. This usage is actually a little bit weird for Chinese
from southern areas.
In the rest provinces of China, 咱 is different from 我。咱 refers to the
both sides of a conversation, and is often used to show closer
relationship or endearment. 咱 is much less frequently used than 我们
there.


So in your example, I think this conversation happens in east-north China since 咱妈 is rare in southern area and it simply refers to 我的妈妈.