You know the OP's mother didn't give the children everything she had, right? She kept the proceeds of the sale of her home (under-market value though it might have been) except for the portion used to build the addition. She also continued to work for some number of years and presumably had control of her own income. Between those two sources of funds (OP never mentioned her Dad's estate, or any pension or SS income) we can assume that's what she's been living off. Her expenses are apparently her portion of the utilities, her own groceries and clothing and her travel.
Although no dollar-amounts have been mentioned, it's been pointed out up-thread that even modest rent, or perhaps even normal taxes and maintenance on the house itself, would have very likely cost her more over the years than her investment in the addition. At that point one can assume she would have been expected to be self-supporting, on whatever income she had. The OP doesn't mention the decision to move her in was primarily financial - on either the mother's part or the OP's. And since the OP also doesn't mention being her conservator, or having POA, one can also assume that being of sound mind and body, the mother could have stayed in her own home if she chose.
I hope
@appleplie will chime in here to correct me if I've misconstrued anything. I'm not advocating for what was done, only trying to bring clarity to the facts as they've been presented. There are so many rabbit trails in this thread now due to people telling their own stories and people posing convoluted hypotheticals, it's become difficult to keep everything straight.