Definitely try feeding the dogs separately to see if that boosts the feeding response of the skinnier dog.
Have your vet check insulin levels, as an excess of insulin production can cause low blood sugar, and can easily be corrected with daily insulin shots. (Tumors in the pancreas can cause insulinoma which can cause low blood sugar.)
Lack of proteins can cause low blood sugar. What do food are you offering, consider a high protein diet like EVO. Dogs need about 30-50% proteins in their daily diet.
If the dog isn't able to eat enough or often enough, low blood sugar can develop. Separating the two dogs during feeding time can potentially correct this.
Abnormal hormone function and productions can cause low blood sugar levels. Addison's disease can cause insufficient secretion of certain hormones which can cause low blood sugar levels.
Your vet should be able to do a blood test to check for hormone levels and insulin.