How to create svg path from right to left / center to sides / or vice versa?

I have a line drawing in png format. I need to create an svg from this line drawing.

I need to create the svg path from right to left, left to right, center to sides OR sides to center...

I'm using a jQuery plugin (lazy line painter), that animates this line drawing in the sequence of the path provided in the svg file.

I'm using Adobe Illustrator CS6, and it creates a jumbled up svg path in the svg file. Due to this, the animation starts and ends abruptly from any direction (as per the svg path in svg file)

I also have the portable version of Inkscape, although I don't know how to use Inkscape to import the png as line vector.

Pleas can someone suggest a way to do this in either Illustrator, Inkscape, or any other utility?

Thanks.