It sounds as if your mother is still living but that due to her age or some incapacity she is not serving as trustee or co-trustee of her trust, is that correct? Also, you say that you would like to buy your sister's one-half of your mother's house; how can you buy your sister's one-half if your mother is living and the house is still owned by your mother's trust - your sister does not own one-half of the house presumably until your mother passes on. In any case, and depending answers to the preceding, the general rule is that the sale by a person of their personal residence will not trigger taxable gain so long as the gain is less than $250,000 for a single person and $500,000 for a couple. For example, if your mother's house cost $50,000 and you purchase it for $200,000, the $150,000 gain would not be taxable if your mother is living and if she did not move into the house less than 2 years ago. If your mother is living, in order to improce the house it may be a better idea for you to make a loan to the trust secured by a mortgage (assuming there are no other mortgages) on the real estate and recorded with the appropriate county office. This way you are sure that when your mother passes you are paid back for the funds loaned to improve the residence - whether you are paid back with cash from the trust or other assets in the trust at the time of your mother's passing. I would encourage you to take the trust and deed to a local trust attorney for a thorough legal opinion with all of the specific facts and circumstances. Another important issue is when a trustee purchases an asset from a trust, there are conflict of interest rules in most state's laws that must be considered if those conflicts are not expressly waived by the terms of the trust agreement.
I hope this has been helpful.