This is a tricky situation. The insurance company seemed to have no idea the client, the writer's mother, was going to sell the house. If so, they could have prorated the insurance till the end of the month she moved.
However, since she paid the bill, moved and didn't realize the error until one year later, a full refund would be unlikely. It was generous that the insurance company gave her a refund for even one month. It would be nice if the insurance company reimbursed the mom for her insurance that was not needed on a home she no longer owned. It is doubtful that they would be legally required to do so. It seems to be an unfortunate error by the insured. She had paid for mortgage insurance for a home she no longer owned.
The lawyer or representative that was present during her home sale closing should have told her about the kinds of insurances she can cancel on the sold home.
Even though the new owners obtained insurance on the home they purchased from the mom, they generally do not inquire about other policies on the home. If it happened to be the same insurance company, they may have realized the address already had coverage and explained that to the client. Since more than likely, it was not the same company, I'm afraid your mother made a costly error and no one is legally responsible for reimbursement of her insurance premium.