Question

Countries whose policies are dictated or heavily influenced by another country are called:

Answer 1

Countries whose policies are dictated or heavily influenced by another country are called satellite.

Answer 2

They are called satellite.
Satellites are objects which gravitate around a planet or another object. Similarly, satellite states are those countries which are only formally independent, however, they rely heavily on another country when it comes to their policies. An example of a satellite country are Poland, Hungary, Romania, etc. during the Cold War (they were influenced by the Soviet Union).