Insulin not only affects glycolysis, it also affects lipolysis. It is one of the regulators of metabolism. Like I said, one of the way lipolysis is turned on/off is by the binding of either insulin or glucagon to a G protein receptor that when activated by glucagon turns on an cAMP cascade to turn on hormone mediated lipolysis enzymes.
Insulin can control metabolism at the level of DNA transcription. Not only does it regulate how glucose can get into cells, it regulates the levels of enzymes that play key roles in glycolysis. Insulin turns the MAPK pathway, which turns on certain transcription factors that increase glucokinase synthesis. GK is the enzyme that controls the first step of glycolysis.
Insulin can also control the levels of fructose 2,6, bisphosphate, the key allosteric regulator of phosphofructokinase 1 which is the major regulatory enzyme of all of glycolysis. Insulin stimulates certain phosphatases that remove Pi from PFK2 and FBPase which causes levels of F2,6P to rise thereby stimulating glycolysis by allosterically turning on PFK1. Insulin does oh so much more than just cause cells to uptake glucose.