I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today. I have been a CA licensed attorney for more than 3 decades.
It is not possible to dismiss a judgment that has already been entered. So that way of dealing with the situation is not going to work for you.
However, under CA law, a small claims party can only appeal a claim/counterclaim made by the other party.
In the case you mention, Plaintiff can only appeal on the counterclaim you filed, not on Plaintiff's original claim that he/she lost.
So, if you as the defendant don't want to deal with it anymore, then just ignore the appeal process. The worst that can happen is that when you don't appear at the appeal hearing, that the judge can rule against you on the counterclaim that you filed---meaning the judgment on your counterclaim would be reversed.
You may reply to me again if you have additional questions, and I will be happy to continue to assist you.
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I wish you and yours well in 2017,