One of the benefits of being an astrophysicist is your weekly email from someone who claims to have 'proven Einstein wrong'.
These either contain no mathematical equations and use phrases such as "it is obvious that..", or they are page after page of complex equations with dozens of scientific terms used in non-traditional ways. They all get deleted pretty quickly, not because astrophysicists are too indoctrinated in established theories, but because none of them acknowledge how theories get replaced.
Then in the early 1900s Einstein proposed a different model known as general relativity. The basic premise of this theory is that gravity is due to the curvature of space and time by masses. Even though Einstein's gravity model is radically different from Newton's, the mathematics of the theory shows that Newton's equations are approximate solutions to Einstein's equations. Everything Newton's gravity predicts, Einstein's does as well. But Einstein also allows us to correctly model black holes, the big bang, the precession of Mercury's orbit, time dilation, and more, all of which have been experimentally validated.
So Einstein trumps Newton. But Einstein's theory is much more difficult to work with than Newton's, so often we just use Newton's equations to calculate things. For example, the motion of satellites, or exoplanets. If we don't need the precision of Einstein's theory, we simply use Newton to get an answer that is "good enough." We may have proven Newton's theory "wrong", but the theory is still as useful and accurate as it ever was.
To begin with, Einstein's gravity will never be proven wrong by a theory. It will be proven wrong by experimental evidence showing that the predictions of general relativity don't work. Einstein's theory didn't supplant Newton's until we had experimental evidence that agreed with Einstein and didn't agree with Newton. So unless you have experimental evidence that clearly contradicts general relativity, claims of "disproving Einstein" will fall on deaf ears.
The other way to trump Einstein would be to develop a theory that clearly shows how Einstein's theory is an approximation of your new theory, or how the experimental tests general relativity has passed are also passed by your theory. Ideally, your new theory will also make new predictions that can be tested in a reasonable way. If you can do that, and can present your ideas clearly, you will be listened to. String theory and entropic gravity are examples of models that try to do just that.
But even if someone succeeds in creating a theory better than Einstein's (and someone almost certainly will), Einstein's theory will still be as valid as it ever was. Einstein won't have been proven wrong, we'll simply understand the limits of his theory.