Your ex-husband can appoint his new wife as "guardian" in his last will and testament, but that appointment is treated as a nomination subject to ratification by a court at that time. The other parent, and perhaps others, would be entitled to due-process notice and opportunity to appear and object.
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Although your former husband may designate his wife as the guardian of the person of the children, in my experience, unless there is a reason that you would not or should not be able to care for the children, they would be transferred to your custody if they are still minors at the time of his death. If he passes away, you should retain an experienced family law attorney to ensure that the transition occurs.
My response is based solely on the limited information contained in the question. It is not meant to substitute your attorney's advice.
I agree with Ms. Silverman. In my experience, as long as you're suitable to be the caretaker of minor children, the court will likely transfer custody of them to you in the event of their father's death. Be sure to contact an attorney if this issue arises or seems imminent. It's better to be prepared as soon as possible. Just because we suggest that it's likely you would receive custody of the children doesn't mean that it must will happen without a fight. In the meantime, be sure to keep to your custody schedule and stay in touch with your children.
Be sure to click Best Answer if you found this helpful. Disclaimer: Please note that this response does not in any way an attorney-client relationship between Kathryn L. Hilbush and the recipient. My responses are general in nature. They do not constitute legal advice. You are advised to consult an attorney regarding this and any other legal matters.