If there is no Will, then the girlfriend's son could not be executor. I would try to discuss this with her again, reminding her of her promises during your father's lifetime. If she still balks, then you may need to hire an attorney. Whether or not you open probate depends on her response. If she refuses to turn things over, probate will be necessary in order for you to get authority to go to the court and compel her to do so. Otherwise, probate is not usually necessary, when there is only personal property. Probate court is all about giving someone legal authority to transfer title to the decedent's assets. In the case of personal belongings, there IS NO title, so probate would not normally need to be involved.
In summary, I would request your father's (and mother's) items from the girlfriend. If she refuses, I would have a lawyer send a demand letter. If she still refuses, you would need to open an estate in order to compel her cooperation.
I am sorry for your loss and wish you the best in resolving this issue!
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Your most desirable course of action would be to resolve this is with the girlfriend. I'm not sure why her family is involved. If you cannot work things out with them, reasonably, you could consult with a local probate attorney. The local attorney can send a demand. If that doesn't work, a probate petition could be filed to compel the girlfriend to do the right thing. Good luck.
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I agree with my colleagues as to your options. I just want to add that probate occurs in the county where the deceased resided. Since Arizona law applies, you should meet or speak with an Arizona probate attorney to determine the best course. A letter from that attorney to the girlfriend might be the way to go.