To those saying the OP should have help caring or maybe involve a care home?
It isn’t always that easy - unless of course you have thousands of pounds of disposable income.
We waited many long weeks for the most basic of help. Working shifts and caring was utterly exhausting. Could I have left it to my other elderly parent who had their own difficulties? Yes. Would that have been a great solution? Absolutely not. So you get on with it.
As for care homes? There are no spaces and it took 11 months to get an assisted living flat.
I suspect there are many thousands of people just getting on with things. Like OP.
As for those who don’t expect 20 year olds to be more aware? Actually I do expect that of a 20 year old. I was aware. My mother was. My grandmother was. My great grandmother was.
The difference is we weren’t treated like children when we hit 16. We were working, (unless in higher education), helping care for elderly relatives and younger siblings because that is what we did. We were not in the minority.
Your niece will be well aware of your life at the moment. It would not have occurred to me to add to someone’s pressures by staying over for a few days - unless I was there to help. Getting home late is not a surprise but it is rude and inconsiderate in the circumstances.
The key? In hindsight, on this occasion, it would have been a great idea but why should she have a key for a house that isn’t hers on a permanent basis?
I don’t see why, as an older adult, OP has to break the ice. I can imagine doing that if I were dealing with a child but that isn’t the case here. Would I do it on this occasion? Perhaps. But I’d give the niece the chance to get in touch first. Hopefully she has had time to reflect.
Going forward OP? Don’t have her stay while you are elbows deep in caring. And after your responsibilities stop or ease? Give yourself a decent break before you entertain houseguests. You deserve that. Caring is such hard work and you need to have a bit of time for yourself.
If it were me? I’d text your niece in a week or so. See how it goes from there. It isn’t worth a permanent fall out.