Frequently Asked Questions - K-3 Visa
Apply for their green card and shoot for a K-3 visa simultaneously.
Once the I-130 is approved and consulate is notified of the approval, they will not issue a K-3. They expect us to wait for the green card approval.
From what I recall, K-3 can be approved at the consulate only until they do not receive official notification of the approval from USCIS. I think it may be too late for your mother. She will probably need to wait for her green card now. That is likely to be quicker than a K-3 at this point, anyway.