I'm really sorry to hear about Snickers' DKA episode, and I'm also sorry that you've all had such a rough time of it over the last few weeks. I hope you'll find the following information and resources helpful.
You need to make sure that Snickers eats enough, has enough insulin, and also be vigilant about addressing any other health issues she has. It goes without saying that you need to keep on top of the URI. It's important to ensure that she has enough antibiotic cover while that resolves.
When you're at the vets ask them to give you a supply of anti-nausea medication (e.g. ondansetron) and also an appetite stimulant (e.g. cyproheptadine) to hold at home so that you can address any inappetence head-on. Hopefully Snickers won't need them but it can make a world of difference having the appropriate treatments available at home should a need arise for them. Here's a helpful link about nausea, vomiting, and effective treatments for same:
Nausea symptom checker and treatment info
These meds can really help a cat recovering from DKA to keep eating if they're having difficulty. Getting sufficient calories into Snickers will be critical to her continued recovery.
Here is a link to a primer on DKA and another link to tips for tempting cats with appetite issues to eat:
FDMB DKA Sticky
Persuading your cat to eat
With the URI on the go, smellier foods might be more appetising to Snickers. Warming the food can help with this. Also, if she's a bit reluctant to eat because she can't smell the food properly try getting her to lick a little food from your hand. Her Jacobson's organ might then pick up the aroma and trigger her interest in finishing the meal.
It is also critical that Snickers gets the right amount of insulin to meet her metabolic needs - and all the more so because she's still recovering from DKA. I agree with the others above who have expressed the view that it would be wiser to make sure that Snickers has 24-hour cover from her insulin and that a 12-12 schedule for Lantus works better. I
strongly recommend you revisit this issue with your vets and agree a dose that will be safe to administer once every 12 hours. You will need to test before each insulin dose. You will also need to get mid-cycle tests as best you can. You advise above that you're out of the house for 10 hours during the day. If you could get an 'in the door' test, preshot test, and 'before bed' test on days when you're not home all day plus a curve on days when you're at home longer all of these data will give you a better picture of how well and how safely the insulin is working for Snickers. I'm glad to see you're going to get a meter and testing supplies. Here are some links to help you learn about home testing, plus a link to the instructions for setting up an FDMB spreadsheet:
Home testing links and tips
Testing and injection tips
FDMB Spreadsheet Instructions
I'd hazard a guess that no caregiver who is confronted with the prospect of caring for a diabetic cat is overjoyed at the prospect of 'making pin cushions' of their little one but it may help to steel your resolve to remind yourself that it's much better than the alternatives that may arise from not testing.

As you develop a routine and make it as much a positive experience for all of you as possible (lots of treats and fusses!) you may actually be surprised at how quickly it becomes part of your daily routine. Many cats here actually 'remind' their humans that it's test time - especially when they work out that it has a lot to do with them feeling better again, plus they get yummy treats and extra attention.
It goes without saying that you'll need to be highly vigilant in monitoring Snickers' ketone levels, so it is VITAL you pick up supplies for testing ketones before Snickers comes home. Most people use urine dipsticks (e.g. Keto-diastix) but there are also blood ketone meters available (used in the same way as a blood glucose meter so you can test for BG and ketones at the same time). The blood ketone meter test strips are on the pricey side but they are worth their weight in gold when nursing a convalescent cat because you can check ketones pretty much at any hour of the day without the need to wait for kitty to produce a urine sample; a lot less worry for you, too. My cat thus far has not been ketone prone but she had an operation recently. When she was in the early days of her post-op recovery she developed an infection and wasn't eating properly (she lost an eye so her face and mouth were very sore, and the antibiotics were upsetting her digestive system). She started producing some ketones but thanks to the real time information I got from her blood ketone meter I was able to help her avoid DKA (she would not have survived the treatment). Can't recommend the ketone meter highly enough for critical care situations.
I hope some of the above will be of help to you. It's a fair bit to take in so pace yourself; I just thought it would be helpful right now for you to have some key links gathered together in one place so you'll be able to find them easily when you need them.
Fingers and paws crossed for Snickers over here in the UK. In the last few years I have been absolutely astounded to discover how resilient cats can be and how well they can recover with the right care and treatment regimen. Don't be shy about asking for help whenever you need it.
Mogs
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