If I've understood your OP correctly, @AnnaQuayInTheUk, your MIL and her husband didn't use all of their money to buy their joint house.
So, with some made up figures to illustrate, her husband had 400k from the sale of his house, she had 600k from the sale of her house, and they jointly bought a house worth 700k to which they each contributed 350k, leaving him with 50k in savings and her with 250k in savings.
Acknowledging that the figures are made up, is that how it worked? They each put an equal amount into the house they bought together?
If that's the case then I think your husband is quite correct. They intended the house to be joint and their savings to be separate, as far as possible.
Your husband and his step brother each got/get an individual inheritance on the death of their own parent (the individual savings) and a joint inheritance (the house) on the death of both their parent and step-parent.
Your husband's stepbrother has had his individual inheritance already because his father has already died, and is still waiting for his share of the joint inheritance. Your husband hasn't had any inheritance yet because his mother is still alive.
Your MIL and her husband clearly didn't intend everything to be completely equal. If they had, they would have transferred all their individual savings into joint savings, or each left their individual savings to the surviving spouse first, and your husband's stepbrother would be yet to receive anything. If they had done that, either a larger share of the money your MIL originally brought to the marriage would have gone to her stepson (if she kept her word and left everything to her son and stepson equally) or her stepson would have got nothing at all (if she'd done the dirty after her husband's death and changed her will to leave everything to her own son).
If she had died first, her husband could have changed his will and left the entire house to his son, leaving your husband with nothing except his mother's individual savings.
Perhaps they were advised to keep the individual savings separate to avoid the risk of either son being (deliberately or accidentally) completely disinherited.
So...
With all that in mind, what you are suggesting is that your husband's stepbrother should part-fund your MIL's care from the joint inheritance he is yet to receive his share of, rather than your husband wholly funding his own mother's care from his own individual inheritance.
And since your MIL brought more money to the marriage than her husband and had a larger individual savings pot than him (meaning that, if neither of them needed any care, your husband would stand to inherit more than his step brother), what you are effectively suggesting is that your husband's stepbrother who was in line to be less well off than your husband should subsidise your MIL's care costs to protect your husband's, larger, inheritance.
Now, if your MIL needs care for a really long time, her individual savings might be exhausted and the house will have to be sold and your husband's stepbrother will end up paying for some of his stepmother's care. But from the way they set things up, I think it is clear that they intended this to be a last resort.
Or to put it another way, your husband's stepbrother would not have shared most of the the financial benefit of your MIL not needing care, so why should he share most of the financial burden of her needing it?
TL;DR, your husband is right.