In Stargate Universe I understand that they can't dial from the ship Destiny to Earth because they don't have enough power. But why can't they dial from Earth to Destiny?
Power plain and simple. Icarus Base was on a planet full of Naquadria, the unstable cousin to Naquadah, the gate material. To produce enough power to make the connection they had to use the planet as a giant reactor. And an unstable one at that.
Dialing back from Destiny has the same problems. The only successful dial home from was by constantly drawing power in from a sun to power the gate and that was unstable. As for the attempt with the seed ship, we don't know how well it would have worked or how long the gate would stay open. The two dialings to Destiny (Icarus and Lucien Alliance) lasted 5min+, dialing from the sun less, and Wray's comment "Very shortly we will be making an attempt to dial Earth. If a successful connection is made, we will need to move quickly." indicates that the power from both ships would only have powered the gate for a short time before leaving both powerless husks.
The Destiny gate was designed well before the other Stargates. As we know, they later modified the gates to have 9 chevrons so that they could actually dial Destiny.
The reason that the Tau'ri can't dial from Earth to Destiny is a lack of power.
Back before the Ancients ascended, Destiny was far closer to Earth - far less power was required to create a wormhole stable enough for use.
Now that Destiny has been flying through the universe for a million years, the power requirements are astronomical, requiring the Tau'ri to connect the gate to the Naquadria core of P4X-351 - there simply isn't any way to provide the power that the gate would need to create a usable wormhole.