How do I know if I've been appointed as executor of an estate?

First, I am sorry for your loss. What a sad situation. 

A Power of Attorney is only valid when a person is alive. The moment your son passed away, the authority granted by the Power of Attorney ended. It sounds like your son was married at the time of his death. There are a lot of moving parts here, and you should really consider talking to a probate lawyer, but the short answer is that a surviving spouse has priority to be the executor of an estate, estranged or not. 

It is also true that you will have no control over finances, the wife will control everything. If you son executed a valid Will, that might help solve the problem. Now it depends on what the Will says, what assets are involved, was property separate or community property, etc. A Will or a Revocable Living Trust would resolve a lot of your questions here. I hope you are able to find some resolution. Please, talk to a probate lawyer before you file anything with the court. The estate claim is strange. If you didn't file, and she is disputing, who filed? You need a plan here, and the lawyer will help you map that out for you. Best of luck.