The Council on Foreign Relations has a good interview up with their Senior Fellow for India, Pakistan and South Asia, Daniel Markey. Here's Markey on Pakistan's goals inside Afghanistan:
The Pakistanis would want to see an Afghanistan run by a collection of individuals who are at least sympathetic to Pakistan and who are committed to not seeing much in the way of Indian influence in Afghanistan. You really do have to trace this back to Pakistani concerns about being confronted on both eastern and western borders by India. Some of that is a bit obsessive, but that's certainly the way the Pakistanis have perceived developments in Afghanistan. They have seen a rising amount of Indian influence and a potential that they would be squeezed by both sides. So they want to make sure that they have preponderant and certainly dominant interests and influence in Kabul into the future. They will probably not be satisfied with anything short of that.
As Markey notes, the way the Pakistanis see their interests protected is by nurturing militant groups that have sheltered international terrorists in the past and would presumably do so again in the future. There's not much our counter-insurgency can do about that, unless we can combine it with a diplomatic effort to change Pakistan's strategic outlook.
