Dan, you will have a pretty long run to your panel. I don't think the crawlspace under the great room is accessible and the direct access is under the deck..... Probably run it in conduit under the soffit to the gabled end of the house and then trench directly across from the shed. I have no idea about panels or any electrical advice except to get an electrician. (But it would be easier, a shorter distance, and therefore cheaper if you pulled it from your in-law's panel........
)
Nice shed by the way!