A: I can't fully answer this without more information. However, if your father had a Will when he died and that Will was admitted to probate then the terms of the Will dictate how the property is distributed. If he died without a will then his wife will acquire 1/2 of the property acquired by "joint industry" of husband and wife during their marriage and an equal part of the non joint industry property split equally with all of his children. Considering this probate has been ongoing for 19 years I would suspect there are bigger issues at play. You should contact a local attorney to discuss further.
A: It could perhaps be considered a conflict, however, there isn't a quick run around a probate. I've assumed this house is in Oklahoma. Assuming the house was titled solely in your brother's name, then there is no way to legally transfer title without an administration of your brother's estate. A title company would not pass title on the house without this administration and therefore no sale would be concluded. You have a right equal to your sister to apply to be administrator of the estate. In Oklahoma, priority of appointment goes first to the surviving spouse, then children, then parents and then to siblings. Assuming none of these other parties exist or assuming they would decline to serve you can apply to be appointed administrator of the estate. Depending on what other real and personal property exists and the value of the estate there may be abbreviated probate procedures of which you could take advantage. You should contact a probate attorney.