[Vuejs]-How to mock a user module differently in each test?

Solved! I had a couple issues, as it turns out:

1. Not properly mocking @/adonis-api. I should mention that it only mocks stuff at the top level, so I had to use a factory function in jest.mock (see below).
2. I needed an await flushPromises() to allow the template to re-render after its created() method evaluated my mock function and stored the result in this.children.

Full test:

import { shallowMount, config } from '@vue/test-utils';
import flushPromises from 'flush-promises';
import OrganizationChildren from './OrganizationChildren.vue';
import { organization } from '@/adonis-api';

jest.mock('@/adonis-api', () => ({
  organization: {
    family: jest.fn(),
  },
}));

describe('OrganizationChildren', () => {
  config.stubs = {
    'el-tag': true,
  };

  it('shows nothing when there are no children', async () => {
    organization.family.mockResolvedValueOnce({
      descendants: [],
    });

    const wrapper = shallowMount(OrganizationChildren, {
      propsData: {
        org: {
          id: 1,
        },
      },
    });

    await flushPromises();
    const h4 = wrapper.find('h4');

    expect(h4.exists()).toBe(false);
  });

  it('shows children when provided', async () => {
    organization.family.mockResolvedValueOnce({
      descendants: [{ name: 'One' }, { name: 'Two' }],
    });

    const wrapper = shallowMount(OrganizationChildren, {
      propsData: {
        org: {
          id: 1,
        },
      },
    });

    await flushPromises();
    const h4 = wrapper.find('h4');
    const list = wrapper.findAll('el-tag-stub');

    expect(h4.exists()).toBe(true);
    expect(list.length).toBe(2);
    expect(list.at(0).text()).toBe('One');
    expect(list.at(1).text()).toBe('Two');
  });
});