Your sister-in-law’s appointment in the power of attorney has nothing to do with inheriting property. In fact, it does not give a person any rights to property at all.
sounds as if the type of POA you’re describing is a general power of attorney for finances. Such documents usually only take effect if the principal becomes unable to make his or her own decisions. They’re called “durable” because they endure in this way. It would allow your sister-in-law only to make decisions about and to manage your brother’s finances if he becomes unable to do so.
Your mother is free to leave her property in whatever way she wishes—by will, trust, or pay-on-death designation for some types of property.
If your mother's will does not specify any executor, then the court will likely appoint one to gather up her property and distribute it according to the terms of her will when she dies. A judge usually makes that decision based on whether a person who petitions to be executor seems to be the best one for the job; in some complicated family situations, an impartial outsider is appointed. And again, the fact that your sister-in-law is named as your brother's agent in his power of attorney should have no effect on this process.
If your mom remains concerned about this, she could consider setting up a trust for her property that also imposes more specific requirements for how the property should be managed and distributed.