A miracle-worker is known by her acts. As are prophets respected from their accuracy. That said, miracle-doers and prophets do exist even in the age of Grace, however the big question is, "Is your Mom one of them?" And if so, the much bigger question is, "Does she get this power from God?"
To each there is a spiritual gift, and one the gifts specified by Paul is that of prophecy, so yes, it does exist. I do believe in prophets. That said, I have a hard time believing that your mother is one, specifically because it is confined to a small area (like your family, and the immediate vicinity). This is because most OT prophets were given visions that had greater consequences and a grander scale than what is provided here. It was never self-oriented nor within their personal sphere, but was always intended to communicate God's word to people much away from their families.
Biblically, Prophecy is usually also linked to a specific function: to rebuke a people, to encourage them, or to warn them of things to come. As far as prosperity prophecies, the only ones I know are those that are about the new covenant. Also, she does not seem to use this "talent" to preach God's Word (only claiming this power is from Him). As such, I have doubts about its origin. Prophecy is different from fortune-telling. As such, these things may simply be a dream from another source, or the popular belief that there's a mind-link between mothers and children, it may also be an extraordinary talent that has no connection with God at all.
That said, I won't jump into conclusions. Let's just wait in case you miraculously become the President of the United States or something in a few years...
That said, make a good research on this new church. Use the Fruit of the Spirit test on it, and see if it is a church that follows the principles of Christ. Arm yourself properly with God's word before going in headlong to hear its deeper doctrines, as you need it to know what is true to the new covenant Christ gave us and what is not. Be well.