My Mum in law also has COPD, and dementia, with the COPD being diagnosed I think about 8 or 10 years before the dementia diagnosis. The combination of the two did cause some issues at times.
We had problems, when Mil was in the early mid-stages and still living in her own home, with her over-using one of her inhalers, that was only supposed to be used 'when needed' and a maximum of 4 times a day. Mil took to using it far more than this, often going through a months supply in a week or less - and she was amazingly creative and crafty about persuading the GP or chemist to issue more of the capsules. You could explain till you were blue in the face that she was going to make herself ill if she didn't take it only as prescribed, and she would either flatly deny over-using it, or insist that 'this doctor she had been to see' had told her she could use it as often as she wanted. When I took her to her COPD review, and told the practice nurse (quietly) about the issue, the nurse spent ages talking to Mil about mis-using/over-using it - Mil pulled the perfect hostess mode out, and the nurse was quite satisfied that she now understood and the issue was resolved!
We also went through a stage where Mil (who also has angina) would have both this inhaler and her GTN spray close to hand, and would often use the GTN when she felt breathless, or the inhaler if she was having an angina attack. When - not surprsingly - this failed to bring her any relief, she would panic, and she dialled 999 on numerous occasions.
These problems were only resolved when we moved Mil in with us. There was no reasoning with her, and the failing memory meant that even if she was initially receptive to our concerns, she would soon forget.
When she moved in, I took over management of both the inhaler and the GTN, and that caused different issues for a while. Mil would furiously demand that I give them to her to manage, and if she did get hold of one or the other, would hide it about her person and go back to using over-using it. At this point she was frequently insisting that these illnesses were going to kill her (though she wasn't obsessive about this) and I would be accused of wanting her to 'die as soon as possible' by either not letting have hold of the inhalers/GTN herself or because I would refuse to let her use them on demand - and she could 'demand' several times an hour. At the secure day centre that she eventually went to, she even managed on a couple of occasions, to nab her inhaler/spray from the medication trolley, and I would later find it either in her handbag - or hidden in her bra, at bedtime!
As the dementia worsened, these problems faded. But what was always horrible was the breathlessness you describe your Mum experiencing, when she got agitated, and Mil got agitated a lot. It was scary, and as she was very resistent to any form of distraction or compassionate communication, all I could do was give the inhaler (if she would allow me to) and continue to try and calm her. Thankfully, as I said, we didn't have the scenario you describe, with her obsessing over going to die at this stage, and I can only feel for you in trying to reassure and deal with that, as well as the agitation .
Mil is now in an EMI nursing home, and the dementia has progressed massively. As its progressed, her awareness of the COPD (and angina) has slowly gone. I don't think she is aware at all of any of her physical health problems. Over the last several months, its clear the COPD is worsening and she is often wheezy - but, she either seems oblivious to the breathing, or she may sometimes attribute it to having 'had a cold'. She still has frequent bouts of agitation (in fact, they have got worse) and staff have said that her breathing remains a big concern when she is 'kicking off'. But, there is nothing they can do. Medication to help with the aggression/agitation doesn't work with her - in fact some that have been tried actually make her worse - and all they can do is try to calm her and try to persuade her to use the inhaler when it's needed (she is becomming increasingly non-compliant with taking meds of any sort).
I have to say that overall though, the COPD (and the angina, and diabetes, and asthma!) have tended to take a back seat to the dementia. And I am like you - I actually think it would be far kinder if she had a sudden and swift heart attack, or if one of her now increasingly frequent chest infections would take her quickly and peacefully xxxx