My diabetic cat is aggressive, warm, and moody. Is she sick?

I would be concerned by the lack of normal urination in a diabetic pet - they are very prone to urinary tract infections due to higher than normal sugar content in their urine which can encourage bacterial infection. I strongly recommend a urine test to determine exactly what is going on. Your vet may have special cat litter to collect a urine sample or may be able to draw a sample directly from the bladder with a needle in order to investigate fully what is going on

Please try to bring her appointment forward to get her rechecked and her blood sugar levels controlled more effectively if possible. It may be necessary to change her insulin type but she should also be checked for infections/inflammation etc which may be altering her ability to regulate her condition

Yes unfortunatley in cases where a diabetic cat is not able to be medicated and maintain hydration, euthanasia is the best option. The fact she has other complicating factors reducing her mobility and causing her discomfort means this may be very soon to prevent suffering. See the following article for information on helping to decide when http://vet.osu.edu/assets/pdf/hospital/companionAnimals/HonoringtheBond/HowDoIKnowWhen.pdf

Since it sounds like this is a recent behavior change for Zora, I would be very suspicious that she may have an underlying medical problem causing her aggressive behavior. There are a number of common problems in older cats that can cause behavior changes like this, including hyperthyroidism, chronic kidney disease, or even pain from arthritis. I would recommend taking Zora to the vet for an exam when you are able to - he/she can do blood work if needed to check for these issues. If a problem is found, it's likely that it can be treated with medication to make her more comfortable and hopefully improve her mood as well :)

You should take Kizzie back to a veterinarian for a proper thorough exam, with a urinalysis and blood work. Diabetes does not often have obvious signs, nor does kidney disease. Both of those can be ruled out with blood tests and urinalysis. Most cats with a UTI do not need antibiotics as most times it is stress induced. All the more it is important to verify that bacteria are involved before prescribing antibiotics. You may want to get a second opinion from another veterinarian.

Yes, I think that you should have Ember checked out by a vet. While diabetes is not terribly common in cats of her age, it is still possible. Other possible causes of increased thirst include kidney disease, UTI, or behavioral change. Diabetes and kidney disease can easily be screened for with routine bloodwork and urinalysis.

Those are tough questions to answer without being there to visualize each cat. But I would say generally speaking whichever cat is acting abnormal. Abnormal behavior can mean anything from the cat being lethargic (lacking energy), vocalizing more, drinking more water, or even going to the litter box more frequently. As far as what illness could be causing this, there isn't enough information as of yet as to what symptoms either cat is displaying besides be increased aggression. Do some monitoring of both cats over the next few days to gather clues and then feel free to repost your question with specifics so that we can discuss some possible causes. However, in general we do worry about kidney and urinary infections in cats. Also a change in mood could indicate an endocrine disorder, brain malfunction or even diabetes. I hope this helps and look forward to more information about your fur babies. I do hope we can figure things out soon and get them to being friends again.