I don't know how financially comfortable you are, so my thoughts are: -
1. If you're comfortable and have enough without your share of the house, then gift it to her. Firstly to avoid all liabilities that seem sure to surface based on your description eg unpaid taxes.
I never said she hasn't paid the property taxes, she always has.
Secondly full-time 24 hour care of an ailing relative is expensive so maybe to feel better about it, think of it as compensation for her lost income.
Ya, she didn't really lose income, she wasn't working and basically was supported by mom while caring for mom. Which is fine.
2. If you don't have much yourself and really need it, then it seems that you're only option is to force it to be sold and split it. Or give it to her on the basis she pays rent of X for so many years and know that you probably won't receive it, but maybe some?
Good luck. Deaths in the family tend to make people nuts.
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As of the latest conversation, I'm waiting to see if her longer work history and possible raise might allow her to get a mortgage. I expect by the end of February I will know the answer.