Desperate Daughter

You say that your mum is eating exactly what the dieticians tell her. Dou you think it's too much carbs for her? might she try reducing her carbs and her insulin to match? If she's losing weight, because her insulin is too low, reducing carbs might help
Losing weight without meaning to may be a result of too little insulin,or of course something else entirely (I'm not a doctor)Type 1 onset at her age is certainly VERY rare. Have they investigated? could it be LADA?, which presents as type 1
If you get hold of a book of nutrition information, the little Collins one isn't very expensive, you could calculate the carbs that your Mum is eating. If there's a lot of bread, rice, potatoes or pasta on the diet sheet, could she try first by just cutting down on portions?
You also say she's having 5 injections, but testing 4 times a day. She should talk to her care team about testing before and after each meal, at least until she's stable. She's an older person, but does she have a young attitude? because she'll probably need it to cope with all this.
I wish her and the rest of our family well

Your mother isn't alone, there are more and more people being diagnosed at an older age. LADA is slowly developing form of type 1, the older the person, the slower it tends to develop. Modern testing and understanding mean that more people are being diagnosed as such rather than being left to fail on type 2 drugs. I was in my 50s and totally confused/bemused.

I've been thinking about how to answer this one. Is actualy very difficult as there are so many variables involved. Your Mum's glucose levels will depend upon her activity levels, her adjustment of her insulin according to her readings, the number of carbohydrates she eats and if she is taking the correct amount of insulin for them. When the balance between them is correct then her BS should be at better levels.

Heres some questions to think about, discuss with the doctor.

She tests 4 times a day, but does she know what her target BS is before and or after meals, does she use the result to adjust her insulin ? If she doesn't know how to do this, then its something to discuss with the doctor.
If her diet is controlled/sugggested then thats one less variable, as long as she is truly eating the correct amount of carbohydrates prescribed in the plan.Its not always easy to estimate, does she use a scale/carb counting book to check? (most people on multiple daily injections learn how to vary their carbohydrate/insulin doseage but when I came out of hospital originally I kept the same number of carbs as prescribed and varied the insulin according to BS level before the meal, this can work very well but is less flexible)
She went to hospital with high ketones. Does she now have ketone testing strips and use them if her BS is over about 14mmol? Does she have a protocol to follow if she has ketones? (ie how much insulin to take to reduce both BS and ketones)
Does she recognise hypos, dose she have glucose tablets/lucozade available at all times and know how much to take?

If you/ your mother want to understand insulin use a very good book (though American) is Using Insulin by John Walsh