Are there affordable agencies to just come and check sugar level then give her the shot?

You live in a funny state. Most ALF are connected to a care and having them do it is a simple thing. Sorry, checking blood glucose is not considered advanced care. I know of grade school kids that do it, never seen in the rules.and regs where it states you must be an RN.
Been in medicine for years, never thought of such tripe. Yes, while simple, most centers now have LPN or higher, years.ago we would train the aides do it, and no problems.

I suspect someone wants to admit someone to ltc, and say advanced care, so they can charge more.

We had one once like that around here, lasted 3 months. Went to a different state.

Busy, ALF's do not do advanced nursing care like glucose samples and drawing up the right amount of insulin and injecting it. The state health laws limit what they can provide in house.

Wait a minute. She is in assisted Living, and they can't figure out what to do, something is very wrong. They could assist her with that. They want her in the nursing home
so they can bill more and make money.

They are lower than a snakes belly

If someone has LOW blood sugar, the worst thing you can do is give insulin!
Insulin is only indicted for HIGH blood sugar, and usually needs a combination of fast acting and long acting, as recommended by the doctor, and once a week doesn't sound appropriate.

Call your State Dept.of Aging and they will come in and do an eval. and set up what is needed.
Mom has a very good PC and I had her there Fri. before last and he had it set up for last Wed. They were very helpful.

Can a neighbor or friend help?

A couple ideas. First on monitoring There are meters that have large numbers and also reads the level
Out loud.

Next option, using ihealth system She can take bg, and it will report To "the cloud". If way out of norm Will contact the Dr or you depending On how set up.

Why can't she give herself a shot. It is simple. If dexterity is a issue there are aids. The is a device that will give the Insulin with a push of a button. Also one that works on air pressure.

Lastly, get her a medical alert with Auto detect. Will go off if she falls Automatically. Also if no activity for So long, will also alert.

Worse comes to worse, adult day care, or assisted living.

The VNA billed $200 for each visit. The ALF can arrange this, but it would be totally out of pocket. Any visiting medical personnel have to be cleared by the ALF administration for liability reasons.