I work in car insurance so please allow me to set the record straight.
The extension that allows you to drive other vehicles only covers you for third party damage, and that vehicle MUST be insured in its own right.
It doesn't matter if you park it up because it would still be insured, and besides you couldn't cause third party damage if you're not driving it.
As per your question, you're absolutely right there. If the vehicle is in your mother's name it would be her car, not yours. However, if you are insured on that policy, your "driving other cars" extension would not apply because you would be covered directly under the vehicle's own policy.
So yes, you've found a loophole, but as others have commented, i strongly doubt it would be economical for you.