You are asking a question involving estate, probate, real estate, and elder care issues. I suggest that you speak with an attorney in person to review the issues. This question presents a number of complex interrelated issues, that do not lend themselves to easy answers, such as in this forum.
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I agree that this problem requires a consultation with a New Jersey attorney. However, I want to try and answer a few questions that are fairly straightforward. First, depending on whether the property was owned as a joint tenancy or a tenancy by the entirety, it is completely true that the property would transfer to the remaining spouse, notwithstanding what was in the will. The law says that property owned in that matter is not "probate" property. So, the will doesn't really play into it.
Similarly, New Jersey (like some other states) has an "elective share" law that says, assuming that the couple was married, the remaining spouse has the right to a certain percentage of the estate and the deceased spouse can't cut him or her out completely.
You are right - this situation is very convoluted. Hopefully this brief explanation has helped sort out a few questions.