I repeat, assumptions are merely the starting point of scientific enquiry. They cannot form the basis of a hypothesis or theory without some concrete evidence to back them up. The half-life of every radio-active isotope is known, and is not a matter of guesswork, conjecture, or assumptions.
If genuine discrepancies have been found within the same rock sample from different isotopes, that would still not constitute proof of the young universe theory unless they were of the order of several billions of years. But if they were that fickle, they would have been abandoned long ago.
Consider another point. If the universe were, say, only 10,000. yrs old, we would not be able to see our own galaxy, nevermind millions of other galaxies. The light from our nearest galactic neighbour, Andromeda, takes some 2.5 million years to reach us, yet we can see galaxies billions of light years away. That would not be possible in a young universe.