Mice usually come in through the outside air vent that is located under cowl. If you remove the cowling, you can put some 1/8" hardware cloth over it to keep them out. From there, they go down into the blower and maybe as far as the ac evaporator. They can’t go any further unless you switch to inside air. Then they can get anywhere in the car.
With the blower motor out, they should have been able to check the cavity before the evaporator for a dead mouse, that is the most likely place that it would be.
How did shop figure out that you ac didn’t work and you didn’t know?