What evidence is there linking melting ice caps and changes in tectonic movement?
Continents move slowly. Glaciations are ephemeral in comparison.

That said, there apparently is a huge connection between plate tectonics and whether the Earth is in icehouse or hothouse conditions. There was very little if any ice on the Earth when the Earth was in hothouse (aka greenhouse) conditions. Dinosaurs roamed close to the poles. The Earth's climate was (and is) considerably cooler during icehouse Earth conditions. Widespread glaciation has only occurred during icehouse Earth conditions. Note that we are currently under icehouse Earth conditions; we just happen to be between glaciations.

The following conditions that contribute to icehouse Earth are all due to plate tectonics:


Having a continent parked over a pole.
For example, Antarctica is currently parked over the South Pole. This is not a sufficient condition, however. Antarctica has been parked over the South Pole for 100 million years or so. The Earth has been in icehouse conditions for the last 30 million or so years, and in ice age conditions for about the last 2.3 million years.
Having significant land masses within 45 degrees of a pole.
With the possible exception of snowball Earth (icehouse Earth gone wild), icehouse conditions need significant amounts of land near a pole. Having one continent parked over the pole but most of the continents close to the equator doesn't create icehouse conditions.
Having relatively low seafloor spreading at midoceanic ridges.
This is crucial, for two reasons. Lots of seafloor spreading means lots of CO2 being released into the oceans and eventually into the atmosphere, thereby enhancing the greenhouse effect. Lots of seafloor spreading also means more and higher midoceanic ridges. This raises the sea level, which in turn increases the amount of Earth's surface covered by water, which in turn decreases the Earth's albedo. Reduced seafloor spreading means reduced CO2 levels, reduced sea level, and increased albedo.
Having oceanic currents keep equatorial regions warm, polar regions cool.
The opening of the Drake Passage about 41 million years ago and the opening of the Tasmanian Gateway about 35 million years ago enabled the cold circum-Antarctic current to form. This is when Antarctica turned from just cold to &lt; expletive deleted > cold. The closure of the Panama seaway between 13 and 2.6 million years was the last nail in the coffin regarding current ice age (as opposed to mere icehouse) conditions.