Hello, I hope you are well. My name is***** am a solicitor advocate and I will be assisting you with your question today. I am very sorry to hear of the problem you are experiencing and I will do my best to help you with this matter.
Sorry to hear of your loss. Please accept my condolences.
NO, there is no oath to be sworn when acting as an executor.
You are appointed as an executor by the person who made the will, in this case your mother.
There is no legal obligation for you to take up the role of executor and as stated above, no oath to be sworn.
The two brothers how are at loggerheads, have no input in to what each receives. This would normally be detailed in the will, if however, the will simply says divided equally then any personal items do become an issue that needs to resolved.
That should be done by the executors.
One way to try and resolve items that more than one person wants is a very simply draw. Enter all the contested items into a pot and each person takes turn drawing an item form the pot and they get to keep that item.