I am having a bit of a hard time telling what mix she could be, but you could be right with the min pincher part. What did the rescue tell you that she was a mix of? - Corgi and What?
And I too would love to see the pics of the brother if you have any or could you post some more views of your new pup. Either way, I am with Jessica, she looks very cute. Whatever mix she is, you have a new friend, and she needs you, so give her a good home, with lots of love, and you will have a wonderful companion - and don't forget the puppy classes.