makes no sense

Yes, the idea of testing once a day makes next to no sense, but many Type 2 are instructed to do so. It seems to be a cost-related issue, but also, some portion of diabetics don't change their behavior regardless of what the test says, so ... need for testing, and learning from the tests is an individual reality.

can a doctor misdiagnose?

Certainly can. Not necessarily in your mom's case. The odds are in the favor of a doctor claiming Type 2 at diagnosis in an older adult; but some percentage of the people here can tell you they got the wrong diagnosis because of that reason -- several new people here each week, indeed. If her new treatment isn't working well -- get more tests and/or another opinion.