Hi. This is Dr. Joey.
If they do keep her all day, then they should be doing a glucose curve to see what her values are every few hours and how she is responding to insulin. A urine recheck is always a good idea. But I'm not sure beyond that much must be rechecked.
Excellent about her thyroid. This will need to be monitored over time because it is possible she was needed more due to being on the edge of diabetes; so her need for thyroid supplement may change.
Liver enlargement can to some extent be due to diabetes; so that should be rechecked perhaps via ultrasound again in the future, once her diabetes is clearly controlled. If there is difficulty controlling her diabetes and both the liver/spleen are enlarged then doing a needle aspiration of the liver would be recommended to rule out cancer as a problem that is causing the difficulty regulating. Also, we must remember SARDs causing a Cushings-like scenario that we do not entirely understand with a lot of the symptoms of Cushing's syndrome such as high ALKP which could make her liver enlarged. For now, though, I recommend focus on controlling diabetes and figuring out the panting.
With regard to the panting, this can be due to many different things ranging from pain to a primary heart problem to a primary lung issue (pneumonia, cancer, etc) and the list continues. This can also be due to the CUshing's-like syndrome from SARDS (hormonally related). So, having your veterinarian do a listen to her heart/lungs and perhaps even chest X-rays may be a good idea.
Sounds like, overall, this is a complicated case and your vet is doing a great job.