Maybe she gave away the £40,000 to her 2 other children - £20,000 each I believe - because the OP's DH had already got £100,000 from her, and would probably not be expected to sell the house when she dies. Therefore, the 2 siblings would be very unlikely to ever get the rest of the approximately £26.6K each, that they should probably rightly get as their inheritance from their DM when she dies.
That choice would really be a no brainer on behalf of a couple with rather loose morals, and who, therefore, wouldn't mind if what they were doing would also rip off their siblings/siblings-in-law ! IMO, the OP and her husband - who have had the great benefit of being able to buy and live in a presumably very nice £1,000,000 property - are not coming out of this scenario very well at the moment.
I honestly don't think that the MiL's large contribution - made by her I'm sure, in order to be able to live with her DS and her DiL, in comfort, and to have their companionship - should now be treated as a fait accompli, and that she is told that she can have a lounge, but it will have to incorporate a tiny kitchen, and that she must not go into the rest of the house in the evenings (and during the day?), as they have decided, after the massive investmentevent that his DM made, that they (both of them or just the DiL) don't enjoy her company, or as she would rightly think, even like her!
That poor woman has, in my opinion, been treated both shoddily and shittedly, by this very selfish pair, and I just don't understand how so many Mumsnetters seem to think that the behaviour of this couple is actually ok, and to even be encouraging them to be even more vile to the woman who brought up the male member of this couple. If the MiL had been a terrible mother to her children when they were growing up, then there is no way that her son would have even contemplated having her come to live with them.
Sadly, I also think that, knowingly or not, @Howdoyousolveaproblemlikemil has been exaggerating about her MiL's behaviour, and that however bad the MiL's words and deeds have been, her DiL would have already been well aware of her MiL's character before agreeing to let her invest in, and move into, a jointly owned property. The living and cooking arrangements between the 3 of them, should have been thrashed out before they even started to look for a suitable home. I think that it would be horrendous of both the OP, and her DH, to now tell his DM that she isn't welcome, and that she has to move out of the home she shares both financially and morally with them, if she won't agree to living in just a tiny part of the house, and to keep herself to herself at nearly all times.
I expect I am about to be lambasted!