The children who are not children of your marriage are collectively entitled to one-half of your wife's sole and separate property. However, I echo my colleagues in not taking any action without first consulting with a probate attorney.
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You need an attorney to help you straighten out what was separate and what was community property. If you wife did not have a will, her property will be distributed according to Arizona's laws of intestacy. You probably have some right to possession over her half of the community property during your lifetime. Don't let her ex tell you otherwise, get your own attorney to protect your interests. Good luck, and I am sorry for your loss.
Reading something on the Internet is NEVER a substitute for consulting with an attorney. No attorney/client relationship exists, and any information you receive is incomplete. It is impossible for any attorney, including myself, to give complete answers without knowing the full background of your situation. You get what you pay for!
I agree with Attorney Sullivan and encourage you to hire an attorney immediately.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.