Legal Question in Real Estate Law in California

After only one year, I wouldn't expect that there would be a lot of equity. I don't know who you want to have rights against, but I don't see anything you could pursue the seller for, nor anything that you could pursue the appraiser for. If there is something wrong with the rec room - like it not being permitted or something, perhaps you might have some claims against the seller.

I'm not sure where you are getting your numbers from. An appraiser would not normally say that one part of a house is worth x and another part y for a total of z. Also, square footage is only one component of what a house is worth, and a fairly minor one at that. What the additional square footage is comprised of makes a huge difference as well. A house with a rec room is probably worth a bit more than one without, but it's not like it's the difference between a two bedroom house and a three bedroom house. You also don't mention whether the appraiser is actually telling you that they over-appraised the house by including the rec room square footage when you bought. Did they actually say that? Are they now saying "ooops" we made a mistake the first time; now we can't include it? Are they appraising it at a different lower value than when you bought it? Too much missing information and things that don't add up to give you much of an answer here.