Amy, it sounds like both you and your mother might have the psychic ability known as precognition -- "knowing" events before they actually happen.
No one really knows how precognition works. We are used to thinking of time as being linear -- one event following another. And if this is true, then no one could possibly know of something that has not happened yet.
Perhaps, however, time it not linear; that is only how we ordinarily perceive it. The flow of time might therefore be only an illusion. There are some philosophers who say that everything -- past, present and future -- is actually happening all at once, and that we only perceive it occurring in a linear way. And if something like this is true, it might explain how some people can "see" or "know" a future event: somehow they are able to break the barrier of linear-perceived time, if only momentarily.
This is all theoretical, of course, but if some people can perceive events before they happen -- and there is a great deal of documentation that this is so -- then reality is far more mysterious, complicated, and wonderful than most people consider it to be.
To get back to your question: How do you hone your precognitive ability? The answer might be as simple as: Listen to it.
If you have a premonition that something will happen (especially if it is potentially dangerous), take it seriously. The feeling might not always be correct, but you should always respect it. After a while, you might be better able to tell which precognitive feelings are valid and which are not.
(This can get us into another whole discussion. Just because a precognitive feeling did not come true, does that mean it was invalid? Or does it mean that time was somehow altered to prevent the event from happening?)
In any case, take your premonitions seriously. Write them down, if you can, so you have a record of where and when you had the feeling. This, too, might help train your mind to tune in to these precognitive feelings.
We even have a premonitions database on this site where you can document your precognitions.