How do I broaden the face without reorienting the picture and therefore losing image quality?
Convert your layer to smart object. Then rotate it so that the wanted stretching direction is horizontal. Rotate it back to the needed angle position. Only the stretching will increase apparent blurriness because the needed deformations are always calculated from that data which was valid just when the smart object was created. Make them as soon as you expect repeating stretchings and rotations to be needed.
You cannot do pixel colors affecting edits to smart objects except with adjustment layers or opening the image inside the object to a different window. For full editability Smart objects must be rasterized. But they are a way to non-destructive deformations and filterings.
ADD: Without smart objects it's possible with warping or in simple cases with Edit > Transform > Distort. Drag the vertical edges of the bounding box to the wanted direction. Be sure you have in move tool options Show Transform Controls =ON
This is useful for small stretches, long stretches like this lose its linearity.
Generally, every time you stretch an image you lose quality.