I'm Doug, and I'm sorry to hear of the confusion.
Yes, under CA law, a domestic partner is granted the same rights as a spouse in terms of qualifying for unemployment in the event that the other partner is forced to relocate for employment. Here is a link to a number of other rights that your partnership confers:
Of the two possibilities, the relocation with your domestic partner for employment reasons is the more likely ground for benefits.
Having to relocate to care for an ill relative may, under the right circumstances, qualify as justification for leaving employment. However, keep in mind that you must be willing to seek full time employment while you are collecting unemployment---so you could not collect unemployment when you can not work because you are caring for an ill family member. Here is a link to the CA law in this regard:
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