This does all sound entirely apt--thank you for sharing : )

The child may learn as an infant/toddler that they must take care of themselves. That they cannot depend on adults for their safety, hence their need for control to make sure they stay safe.
We probably saw this happening right in TIA/DotM--she calls and calls for help and who shows up? Her worst nightmare . . . and her parents. Who don't know who she is, are associating with the Doctor, and as you say, her mother shot her. Then she ran away.