Hypo- and hyperglycemia?

I'm not sure if this is where I should post this, but I figured you all would know the most about it. My mom is underweight, and she has other health issues.

Is it possible for someone to have issues with both hypoglycemia and hyperglycemia? She's had bouts of low blood sugar, that required hospitalized. (Lowest was 13, there was another that was 27). But with testing her lately, even after being a bit low, here blood sugar would spike to like 200 after just a couple drinks of soda. She doesn't take any medicine for her blood sugar, the doctors were saying it was because she was underweight.

I'm not sure what to do, and I'm gonna bring it up to her doctor at the next checkup. But should I be more focused on making sure her sugars don't go too low, or too high? As it's difficult to find a happy middle right now.