Python Unit Testing with Unordered Set for Tree Data Structure

Background

I am trying to add unit tests for a tree data structure I am building (python 3). The tree structure uses sets (unordered) and I am struggling to find ways to test certain methods of my tree class.

Example

Given the diagramed tree...I have a method that will detach a node (say #2) and then choose one of it's children (3 or 4) to take it's place instead of parenting them both to node 1. (This is useful in the case that say #2 is the root and we still want 3 and 4 to be related when 2 is discarded.)

      1----------+                     2        1----------+
      |          |                              |          |
  +---2---+      |    Detaching Node "2"        3---+      |
  |       |      11        -->                 /|\  |      11
  3       4     /| \                          5 6 7 |     /| \
 /|\     /|\  12 13 14                              4   12 13 14
5 6 7   8 9 10                                     /|\
                                                  8 9 10

The Problem

Sets are unordered and the way I select the child (out of 3 and 4) is to check if node 2 has children, then pop off a child from his set of children and make that the one. Because sets are unordered, I get (seemingly) random results in my test cases when I pop the child off.

Question

What should my strategy be to test a method like this (I've read about testing difficulties when using the random module, but I've also read that sets do have some sort of a predictable order)? Should I just test around this problem? Should I try to figure out what order the set will be "popped" in?