Evidence for the Moon creating tides

she has no idea what "proof means"

Newtons laws ( good guesses) about gravity and motion predict the existence of tides in water and solid land and air
there predictions correspond to observation ALMOST always but fine corrections had to be made by Einstein's General Relativity
Newton said he could measure the size of gravity force but had NO IDEA what caused it

the rate of the tides coincides with the moon coming over
also, the tides are stronger when the moon is closer to the earth (we can observe this since the moons orbit around the earth is elliptical)

Tie her to an anchor in the bay and tell her to watch how high the moon is in the sky, when it's at it's highest is when the tide will be high.

She's probably just trying to be difficult.

Observation. Watch the tides and make a chart. Watch the moon's orbit and make a graph on the same chart. Two graphs - Tide and moon's orbit. you will see they are in sync.