If you assign damage to a unit during Battlefield Phase, enough to kill him, and for this example you have 2 more damage to apply to the capital so that is where you assign it.

If a card is played like Blessing of Valaya, which redirects damage dealt to the unit and this is played between the assign and apply phase, and therefore saves the unit from being destroyed, what happens to the damage assigned to the capital. Does it get cancelled or does it still get applied because enough damage was assigned to the unit to kill it, but was saved by a tactic after damage was assigned?

The rule for assigning damage applies when damage is assigned. So, you assigned 2 damage to kill the unit then 2 damage on capital. If after that, the 2 damage to kill the unit is redirected, it does NOT affect the 2 damage assigned to the capital (so that damage still hits the capital).

btw, this should be posted under rules questions subforum so in the future please post questions like this there.