Any ideas on how to handle mum's denial?

Best answer for Mom is to say "I am sorry to hear that" and not get pulled in by this. Eventually push will come to shove with a hospital admission for some mishap that is transport by an ambulance. If you are POA you can discuss with your Mom's MD ways to get her in for testing, but if she refuses you have met the brick wall again. This is very common in early alzheimer's, the thought you ARE being stolen from or the thought that you may be stolen from. From early infancy our "stuff" is of crucial importance to us, and the protection of "our stuff". There is no one on AgingCare involved with an elder who isn't aware of this and hasn't lived with a lot of it. My husband's Mom was so constant in this "Wilma took it" regarding her beloved housekeeper of many years that now, ourselves in our late 70s and early 80s respectively, when something goes missing we say "Wilma took it". The fact that your Mom's denial was so adamant and so infuriated is another sign that you have likely pegged this correctly. If you posited this with gentleness (ie: "Mom, you have come up with so many missing things of late, and they are usually things no one could possibly want, that it makes me think you might be mislaying things more? Are you noticing any things that might concern you with memory? I certainly do as I age." ) and Mom STILL reacts very badly, then likely you are touching on a nerve; she recognizes some things are changing and has looped into denial.
I wish you luck. As I said, eventually you will notice things that MUST BE ADDRESSED. The NYT had a recent article in business section about the fact it is now believed that our executive functions may "go" slowly over 6 years time BEFORE we are diagnosied with dementia of any kind. Scary thought that.

Your mother tells you she's upset because someone has whipped her yarn and crochet needle.

You couldn't bring yourself to say "oh dear, that's a shame. I should ask Young Carer about it tomorrow, perhaps she'll know what happened."

No. You had to be honest and tell this lady, who is already upset, that she has all the signs of dementia and nobody is stealing from her. You even throw in a belittling of her hobby, for good measure. Her wool and her crochet needle are stupid - nobody else would even want them, only you, you daft old bat.

And this was aimed at calming her down, was it?

Who's sending the carers? I should give them a call, explain that your mother is making accusations which you are *sure* are unfounded, and discuss what can be done to reassure her.

As for getting medical input: if you have her permission, you can call her GP and book a telephone consultation which might at least get some balls rolling (though at the moment, don't be surprised if no one wants to do anything).

As you found out, honesty may not be the best policy. Your mom is telling you something she firmly believes in, that things are being stolen from her. She's not in denial. Delusions, believing something that is not true, can be a sign of dementia, but may not be dementia. There are other causes of delusions. The only way to know is to have her screened for dementia by her doctor. If she's homebound and can't get out, you may want to get a social worker involved who has experience with dementia symptoms.

Instead of being “honest” with her, acknowledge her concerns by asking her to tell you more and validating her reality. “What's missing”, or “when did you notice they were missing”, may show her that you're not dismissing her concerns. Another approach may be to say, “I can hear you're concerned, mom, I'll talk to the staff about it”.

Why can't u get Mom to a doctor? Can you get a doctor to her?
I think Mom should have a good physical. Labs to rule out any physical thing causing her to act this way. Then a neurological test to rule out or confirm Dementia.

I know when I can't find something, my first thought is that someone has pinched it - be it a pen, book, keys... until I apply thought and retrace my steps to realise my ridiculousness.
But that skill is not working in dementia sufferers, so the initial observation stands (and probably grows) to crisis proportions where any contradiction will seem confrontational.
Perhaps saying you will ask the carers or have a look next time you visit will defuse immediate concerns (call off the SWAT team!) by which time it will be forgotten or replaced with some new pilfering claim.
The price of being right might just be too high for you in this regard. I tried labeling drawers for my dad's items only to find no correlation to their contents anyway after a few weeks! Things just seem to move around...