The "down side" to providing prednisone on a short-term to an elderly person is that it will shut down the immune system, making them vulnerable to infection, the flu, and pneumonia. The "upside" is that the drug will calm down a "twitchy" lung, and enable the lungs to exist for a few days without albuterol, which results in them regaining a bit of sensitivity to this medication. The question should also be asked "is there a cardiac componant" to the difficulty in breathing. Fluid in the lungs, for example, is often a result of excessive preload due to heart problems. There is no easy resolution, and the administration of pednisone is always a question of risk vs. benefit.
I am going to revise that advice, based on the input of a physician friend. He suggests if she has never been on prednisone to start her on 10 mg, just to see if she is in the category of those who are "supersensitive". I mentioned 30 mg because that much is necessary to stop a truly life-threatening situation.
You have to be on the look put for adverse reactions to prednisone. A certain universe of individuals have big problems with systemic steroids, even in the short run. The thing to remember is that if albuterol sulfate is not working you may be at the end of the line unless you are at a hospital to be intubated. If the "emergency inhaler" does not work you can end up with a "locked lung" which can result in death.
The textbook answer is "absolutely not". But my answer would be there is no significant harm in doing so. The problem with albuterol is that the cells become de-sensitized to the chemical, and suddenly it doesn't work at all. Sometimes a short "holiday" from albuterol will cause the cells to reset. You mom has what is sometimes called a "twitchy" lung. And it has to be de-sensitized. Often a single week or two of prednisone will do the job. Look into getting a long-acting beta agonist such as Formetrol. A bit expensive, but some people do quite well on this. Remember that the half-life of drugs is extended in those over sixty-five. As far as a dose goes, if she is 100 pounds, starting her on thirty mg in two divided doses if she is severely twitchy, then the next day dropping by five until by the second week she is on 10 mg a day, in two divided doses. Meanwhile stay away from the albuterol sulfate. You are trying to clear the cells of this substance. Prednisone causes bone changes, adrenal changes and behavioral changes, but for the short-term "settling" of a really twitchy lung it's the only game in town.