According to the manufacturer, you should not dilute glargine. Glargine also forms a cloudy precipitate when mixed; it is no longer a clear solution. Mixing in the bottle is not recommended because of problems with accuracy of dosing when the insulin is a precipitate, bacterial contamination and the unknown effect on stability and efficacy. See the section "Administration of small doses of glargine and detemir: dilution and insulin dosing pens" in the attached file, "Management of Diabetic Cats with Long-acting Insulin":
management of diabetic cats.pdf (The section starts on p. 255.) In addition, I seriously doubt that the vet diluted the insulin under completely sterile conditions. Unless the dilution was done under laboratory sterile conditions, you risk bacterial contamination.
It can be hard to tell if a diabetic cat has a UTI. Often, they are urinating more frequently but that also happens with diabetes. The cat may be uncomfortable when urinating or there's also a possibility of blood in the urine. Unless there's a lot of blood, the only way it may be visible is with a urinalysis. I would also suggest getting a blood panel run to make sure that your cat doesn't have some sort of infection.I'm also guessing that your vet didn't take a good look at your cat's teeth. Dental problems are the most common reason for a cat to fall out of remission.
