I do not think, generally, adult children do see their parents home as an inheritance rather than a home, but one would need to be completely purblind as our parent's get older not to realise that when they die we are likely to receive some of their assets and in some cases the value of these can be considerable.
Teresa May may have lost both her parents by the time she was 25, but her experience is, thankfully, exceptional. Nowadays, the majority of people are nearing retirement age or retired when their parents dies, and no matter how much financial foresight one has in planning and saving for retirement, few of us could deny that the receipt of a lump sum of money as we go into retirement is a great peace of mind issue; knowing that you have control over what type of care home you go into, if you do, because you are self-funding, or knowing you can afford alterations to your house or to buy in help if required. That doesn't mean while our parents live we look at their assets with £ signs in our eyes
However, the mean, the grasping and the avaricious are always with us and they will be like that in every aspect of their lives, including seeing their parents assets as theirs to covet
I hasten to add, is not what I think is happening in this case. I think bytheway's DiL is more upset by what she sees is the breakdown in trust between parent and child, and that the nature of her mother's new relationship is, perhaps, contributing to a loosening of the mother and daughter bond. The upset over the lost inheritance is a symptom, not a cause.