The concept you're describing, where the Moon is "leashed" to Earth's core and lunar drift is caused by a weakening Earth core, does not align with our current scientific understanding.
Gravity is a fundamental force of nature and is not controllable by humans. It is a force that attracts objects with mass toward each other. In the case of Earth and the Moon, their gravitational interaction is what keeps the Moon in orbit around the Earth.
The Moon's orbit around the Earth is primarily governed by the combined gravitational forces between the two bodies. While the Earth's core does have an influence on the overall mass distribution of the planet, changes in the Earth's core would not directly result in significant changes to the Moon's orbit.
Lunar drift, or the gradual increase in the Moon's average distance from the Earth over time, is a natural phenomenon caused by various factors. One of the main causes is tidal forces. The gravitational interaction between the Earth and the Moon creates tidal bulges on both bodies. The gravitational pull of these bulges causes a transfer of angular momentum between the Earth and the Moon, leading to a gradual increase in the Moon's distance from the Earth.
Other factors, such as the gravitational influence of the Sun and other celestial bodies, also play a role in the complex dynamics of the Earth-Moon system. However, these factors do not involve controlling gravity but rather understanding and modeling the interactions between celestial bodies in a gravitational field.
In summary, gravity is not a controllable force, and the Moon's orbit and lunar drift are primarily governed by the gravitational interaction between the Earth and the Moon, as well as other celestial bodies. Changes in the Earth's core would not directly cause significant changes to the Moon's orbit.