The problem is how your looking for input, or rather the way your doing it. You need to change your code so that more than one key can be detected at once. Using your code above, it would look like this:
Func _process(delta):
var rot = get_rot()
# Move left and right, but not at the same time. If both keys are pressed, then we will move right!
if Input.is_action_pressed("KEY_RIGHT"):
set_rotd(get_rotd() - trav * delta)
elif Input.is_action_pressed("KEY_LEFT"):
set_rotd(get_rotd() + trav * delta)
# Move up and down, but not at the same time. If both keys are pressed, then we will move forward!
if Input.is_action_pressed("KEY_UP"):
vel = Vector2(sin(rot), cos(rot)) * speed;
elif Input.is_action_pressed("KEY_DOWN"):
vel = Vector2(sin(rot), cos(rot)) * speed * -1;
# Other stuff...
As far as normalization goes, it takes a vector and clamps it's values from 0-1, sorta. I would recommend searching vector math, specifically normalization for more detail if your curious. In this case, normalization isn't the problem, but rather the problem is how your 'if' and 'elif' statements are setup.