Being able to trust your vet is essential. They may not be telling you everything simply because there's a lot going on, the onset of diabetes combined with an infection can lead to much worse things. Being "stable" is a general term, I would leave her there where they are prepared for the unforeseen things you cannot treat at home. Everyone wants their cat to come home but these are not Baby Girl's last days, she just got whacked with a completely treatable medical condition. I've had many cats over the last 40 years so I actually do know how you feel, many of us have been there. Be thankful it was not some enormous tumor, she just needs the kind of care you can't give her at home and frankly you'll feel a lot worse racing to an emergency clinic on Sunday night if things go badly.
There is evidence that while dogs are always happy to be visited some cats have a negative reaction to being left behind.
What Lucy (Squalliesmom) suggested about familiar scents and objects makes perfect sense. If your anxiety is getting to be too much ask for a sit-down with the vet and have them explain all your questions. It's a sad fact that when we leave our babies behind they are just one of possibly many other cats and dogs.
Against our vets wishes we did visit with Andrew and everything after that went better but that was just us.
You need to have faith in your vet and established medicine as much as you want to squeeze her right now and take her home. If it's just killing you, and it sounds like it is, see if you can have a video link set up but please don't expect a 24 hour feed.
If all goes well and she is coming home Monday maybe you can sneak in a visit on Sunday.
After that there are hundreds of people here that can give you real and practical advice for the next 10 years of your lives together, we will not abandon you.
Get some sleep this weekend and we'll give you a shopping list for Monday. And when I said "the next 10 years of your lives together" there are plenty of people here with happy cats 20 years or older. I had one lucky boy that lived to 23.
Welcome to the club, crying is allowed. My name is Dickson, not Noah. Soon enough you'll have lots of new friends many of whom you'll remember for a very long time.
Feeling any better now?